Discuss About The Importance Of Time Value Of Money In Financial Management Decision Making

The Theory Behind Time Value of Money

Discuss about the Importance Of Time Value Of Money In Financial Management Decision Making.

1. Concept of time value of money (TVM)

The concept of time value is an economics concept also widely used in the discipline of Financial Management for the purpose of decision making. The theory behind the TVM is used to find out the future value of the money in present time period. In other words, TVM is about finding the worth of a sum of money in present date as its equivalent in future dates considering the effects of interest, inflation and other factors on the money if it is kept until that future date. The assumption behind this concept is that, due to the potential earning capacity a sum of money is worth more in the present than in the future.

TVM is also called as the discounted value of the money or the Net Present Value (NPV). As a matter of fact a rational investor would want to receive a sum of money in the present date as compared to a future date because the sooner the money is received the more value it gives. It gives quantitative value to an assumption or plan which makes it easy to make decisions.The five variables that are used for the TVM are;

• Present value(PV) or the amount in hand
• Future value or the equivalent of the PV in future
• Time period or number of periods money is to be held
• Interest rate or the discounting rate
• Payment or installments (Woodruff 2018)

The formula for calculating the TVM based in the above variables is;

FV = PV x [ 1 + (i / n) ] ^{(n x t)}

1. Discounting VS Compounding process

• Discounting:

Discounting is the indirect assessment of the present value of a sum of money to be received in future. It can also be used to assess the amount to be invested in present so as to receive certain amount at a later date. The concept is futuristic and helps to make decisions for future by determining the value of sum receivable or current value of sum to be invested (Keythman 2015)

A denomination of money is worth more as of today than at a specified future date or even tomorrow. Discounting helps in ascertaining the worth of future cash flows in the present date and gives a clear idea whether or not the target is going to be achieved. Another use of the process of discounting is that it helps in the valuation of financial assets. For example, the current value of a bond is the present value and the value of the same bond in some future date is the future value. The net present value is determined by finding out the difference between the two values using a discounting rate.

• Compounding:

The Five Variables Used in TVM

Process of compounding presents a stark contrast to the process of discounting. This is a direct concept of the time value of money. It helps in determining the future value of the current investment i.e. to say the potential amount that will be received in a future date if we invest today. Also it can be used for the purpose of calculating the payments to be made at a future date for an existing loan or a loan to be taken.

Unlike discounting here we know the present value of money and the future value is to be ascertained. Compounding occurs when the earnings to an asset in the form of interest or capital gains are invested again. The result will be additional earnings in the form of compound interest on the reinvested amount and the original amount.

• Discounting over compounding:

Discounting is the most favored process in the concept of TVM for the purpose of financial decision making because it gives an overview on the current value of money considering all the factors that can come to play in future. It is a comprehensive method of calculating the worth of an asset which considers the inflation, interest rates, depreciation for depreciable assets and taxes. It provides better insights into the present so as to make informed decisions for the future (Sanders 2017)It is wise to use discounting in place of compounding since decisions are made as per the targets to be achieved and the target in the form of future value is known in the discounting process and the current course of action can be decided in the form of a present value (Surbhi 2015)

1. Discount rate and its components

The discount rate is the rate of return used to calculate the present value of the future cash flows in the discounted cash flow analysis. The rate of discounting considers two elements for calculation of an appropriate discount rate; one is the risk free rate and the other being the risk premium. Risk free rate means the receipt that has no chance of default like the rate of return in the government securities. So to construct a suitable rate for discounting, risk free rate is often extracted from the rate of return of the government securities (Dalfard 2016) The risk premium, however, is the risk that the business is exposed to during its operation. The risk factor could differ as per the instrument of investment as it is mentioned earlier that each investment has a unique risk element attached to it. While calculating the premium inflation is often considered as a part of risk. The risk premium is calculated upon consideration of the following factors

• Size of the company
• Industry specific risk element
• Inflation attribute
• Company specific risk element.

Discounting and its Importance

The formula for calculating the discount rate is:

1. Use of different rates for different investment decisions:

It is important to use different rates for different investments because every investment is exposed to unique risk factor(s) and they will have different returns. For a specific investment the risk and return associated with that particular investment must be considered to make the correct decisions otherwise if an incorrect rate is used the decisions will automatically be incorrect. For example, an equity investment must consider the risk premium of the company and industry from which the equity is to be bought and the rate meant for any other company cannot be used to make an informed decision. One decision affects the series of operations and other decisions as well, so for everything to fall in a line it is important to use the relevant discount rate.

1. TVM in valuation of financial instruments

Financial instruments such as bonds, equity and preference shares are the most common forms of investment. To find the worth of each financial instrument and deciding the most beneficial course of action before investing into any of them the concept of TVM is very helpful. This is in reference to a household investor (Larson 2015)

 The valuation of an instrument is a very crucial decision for any company. TVM can help find the valuation or pricing to be fixed for the instrument in question. The pricing is decided based on the factors like taxes, interest, scrap value, repairs and other cash flows. Financial instruments are carried at fair value and the fair value is nothing else but the time value of the investment on the financial instrument. The yield of an instrument is calculated based on the market scenario and assumptions for the future and that yield is then used to calculate the present value.

1. Capital budgeting decisions and TVM

TVM can help in finding out whether an investment will yield positive or negative result. The concept is technical but worth the complication and it can be done in the spreadsheet. The business unit wishes to forecast the viability of an investment in a project, expansion or buying an asset. An investment made now will fetch returns after a few years. Time value concept will accurately tell the worth of the investment in terms of the present value for helping the business unit decide on whether or not to invest in the project. For making capital budgeting decisions the company calculates the cash flows in the form of inflows and the outflows. Then the net cash flow is discounted to estimate the current worth of a future project in the form of the net present value thus found. It can be represented in a formula as under (Merittt 2015)

Process of Compounding

NPV = C x {(1 – (1 + R)^-T) / R} − Initial Investment (Freedman 2018)

1. Other  issues in TVM

The following are the issues when it comes to the use of TVM in financial management decision making:

• The method of finding the present value involves technicality and expertise. It is in itself a process to be learned to be applied.
• Identifying the correct future cash flows of a project and the timing factor involved to earn the return is complicated (Dalfard 2016)
• There are always a minimum of four variables to be ascertained and the variables keep changing as per the current and the future market scenario.
• The normal human mind works as per the growth model but the TVM is based on the regressive model of discounting which is just the opposite of human psychology.

Studebaker seems to be looking on following financial goals:-

Diversification

Buy and hold

Diversification is a technique of investment in such a way your investment do not directly associate with market ups and down, that simply means to not to put all eggs in one basket, so that if you invest in only one company or one kind of investment and if such company falls then in such case value of entire investment will also fall down, diversification allows to keep portfolio in a less risky position. Diversification is a evolution strategy that exploits on market chances by dealing outlay risk over dissimilar asset modules. Diversification tells for spreading the selection among unlike  assets which also includes stocks, bonds, real land, international hoards, and cash equals. Through modification the investment will be able to comprimise on the losses on the profits.

Buy and hold policy is opted to get good returns in long run instead of involving in day to day speculation, in buy and hold policy one need to properly check about ways to investment before investing and less attention is required in buy and hold policy.

In our opinion policy opted by Studebaker are beneficial for him and both are correct goal.It will help in future

In Life Insurance Policy the Sum Invested will keep on Increasing every year with 6% return and that return will increase the amount of investment in the beginning of each year,  hence Life Insurance Policy Sum can be calculated as follows:-

Year	Life Insurance Policy Value at Opening of the year (Figures in $)	Return earned at the rate of 6% during the year (Figures in $)	Life Insurance Policy Value at Closing of the year (Figures in $)
1	550,000	33,000	583,000
2	583,000	34,980	617,980
3	617,980	37,079	655,059
4	655,059	39,304	694,362
5	694,362	41,662	736,024
6	736,024	44,161	780,186
7	780,186	46,811	826,997
8	826,997	49,620	876,616
9	876,616	52,597	929,213
10	929,213	55,753	984,966
11	984,966	59,098	1,044,064
12	1,044,064	62,644	1,106,708
13	1,106,708	66,402	1,173,111
14	1,173,111	70,387	1,243,497
15	1,243,497	74,610	1,318,107
16	1,318,107	79,086	1,397,193
17	1,397,193	83,832	1,481,025
18	1,481,025	88,862	1,569,887
19	1,569,887	94,193	1,664,080
20	1,664,080	99,845	1,763,925

As calculated above, Morton has worked out in same way.

In order to reposition the equity in his home, Studebaker would have to take out a 30-

year, $705,000 mortgage at 9 percent. Explain how the yearly mortgage payments on

this loan were obtained. If the loan is for only 20 years, what would be the annual

repayment?

For calculating Installment following Formula is used

Installment = [P * r * ( 1 + r )^N] / [ ( 1 + r )^N – 1 ]

Installment  = [450000 * 0.09 * ( 1 + 0.09 )^20] / [ ( 1 + 0.09 )^20 – 1 ]

By Solving above equation Installment Comes to $77230.26.

Year	Opening Balance (Figures in $)	Installment (Figures in $)	Interest Payment (Figures in $)	Principle Repayment (Figures in $)	Closing Balance (Figures in $)
1	705000.00	77230.26	63450.00	13780.26	691219.74
2	691219.74	77230.26	62209.78	15020.48	676199.26
3	676199.26	77230.26	60857.93	16372.33	659826.93
4	659826.93	77230.26	59384.42	17845.84	641981.09
5	641981.09	77230.26	57778.30	19451.96	622529.13
6	622529.13	77230.26	56027.62	21202.64	601326.49
7	601326.49	77230.26	54119.38	23110.88	578215.62
8	578215.62	77230.26	52039.41	25190.85	553024.76
9	553024.76	77230.26	49772.23	27458.03	525566.73
10	525566.73	77230.26	47301.01	29929.25	495637.48
11	495637.48	77230.26	44607.37	32622.89	463014.59
12	463014.59	77230.26	41671.31	35558.95	427455.64
13	427455.64	77230.26	38471.01	38759.25	388696.39
14	388696.39	77230.26	34982.68	42247.58	346448.81
15	346448.81	77230.26	31180.39	46049.87	300398.94
16	300398.94	77230.26	27035.90	50194.36	250204.59
17	250204.59	77230.26	22518.41	54711.85	195492.74
18	195492.74	77230.26	17594.35	59635.91	135856.82
19	135856.82	77230.26	12227.11	65003.15	70853.68
20	70853.68	77230.26	6376.83	70853.43	0.25

For the 9 percent mortgage in Exhibit 4, find the loan balance at the end of years 19

Why use Discounting Over Compounding

and 20?

Balance at the end of year 19 would be $466986.66 and at the end of year 20 would be $440393.33, which is calculated as follows :-

Amortization of Studenbaker’s 705000 /-  9  % Mortgage, 30 Years loan
End of Year	Opening Balance (Figures in $)	Installment (Figures in $)	Interest Payment (Figures in $)	Principle Repayment (Figures in $)	Closing Balance (Figures in $)
1	705000.00	68622	63450.00	5172.13	699827.87
2	699827.87	68622	62984.51	5637.62	694190.25
3	694190.25	68622	62477.12	6145.00	688045.25
4	688045.25	68622	61924.07	6698.06	681347.19
5	681347.19	68622	61321.25	7300.88	674046.31
6	674046.31	68622	60664.17	7957.96	666088.35
7	666088.35	68622	59947.95	8674.18	657414.18
8	657414.18	68622	59167.28	9454.85	647959.33
9	647959.33	68622	58316.34	10305.79	637653.54
10	637653.54	68622	57388.82	11233.31	626420.23
11	626420.23	68622	56377.82	12244.31	614175.92
12	614175.92	68622	55275.83	13346.29	600829.63
13	600829.63	68622	54074.67	14547.46	586282.16
14	586282.16	68622	52765.39	15856.73	570425.43
15	570425.43	68622	51338.29	17283.84	553141.59
16	553141.59	68622	49782.74	18839.38	534302.21
17	534302.21	68622	48087.20	20534.93	513767.28
18	513767.28	68622	46239.06	22383.07	491384.21
19	491384.21	68622	44224.58	24397.55	466986.66
20	466986.66	68622	42028.80	26593.33	440393.33

Exhibit 3 indicates that $1,763,925 will be accumulated after 20 years in the life

insurance policy. Is this really true? (Hint: If Studebaker were to make this investment, what would his debt position look like in year 20?)

Yes, it is true, life insurance policy will be accumulated after 20 years to $1,763,925/- as indicated in Exhibit 3, and as calculated in Answer of Question 1, however if Studebaker will opt the suggestion of Morton, Studebaker will have to take loan further for $250000/-, and that amount mortgage Loan will be repaid till the end of 30 years and balance of loan at the time of maturity of LIC (i.e. at the end of 20 years) would be $440393.33/-.

(A) If the excess $300,000 were invested in a long-term asset yielding 8 percent a year,how much would be accumulated after 20 years?

Answer :- $1,398,287, will be accumulated after 20 Years, Calculation is as follows:-

End of Year	Long Term Assets Value at Opening of the year (Figures in $)	Return earned at the rate of 8% during the year (Figures in $)	Long Term Assets  Value at Closing of the year (Figures in $)
1	300,000	24,000	324,000
2	324,000	25,920	349,920
3	349,920	27,994	377,914
4	377,914	30,233	408,147
5	408,147	32,652	440,798
6	440,798	35,264	476,062
7	476,062	38,085	514,147
8	514,147	41,132	555,279
9	555,279	44,422	599,701
10	599,701	47,976	647,677
11	647,677	51,814	699,492
12	699,492	55,959	755,451
13	755,451	60,436	815,887
14	815,887	65,271	881,158
15	881,158	70,493	951,651
16	951,651	76,132	1,027,783
17	1,027,783	82,223	1,110,005
18	1,110,005	88,800	1,198,806
19	1,198,806	95,904	1,294,710
20	1,294,710	103,577	1,398,287

(B) Suppose Studebaker placed $26,145.31 a year into a long-term investment paying 8

percent a year. How much would be accumulated after 20 years (amounts invested

at the end of each year)?

$1,292,178/- will be accumulated after 20 Years, if Studebaker Invests $26145.31/- every year together will earlier Investment, Calculation is as follows:-

End of Year	Long Term Assets Value at Opening of the year (Figures in $)	Return earned at the rate of 8% during the year (Figures in $)	Long Term Assets  Value at Closing of the year (Figures in $)
1	26,145	2,092	28,237
2	54,382	4,351	58,733
3	84,878	6,790	91,668
4	117,814	9,425	127,239
5	153,384	12,271	165,655
6	191,800	15,344	207,144
7	233,289	18,663	251,953
8	278,098	22,248	300,346
9	326,491	26,119	352,610
10	378,756	30,300	409,056
11	435,201	34,816	470,018
12	496,163	39,693	535,856
13	562,001	44,960	606,961
14	633,107	50,649	683,755
15	709,900	56,792	766,692
16	792,838	63,427	856,265
17	882,410	70,593	953,003
18	979,148	78,332	1,057,480
19	1,083,625	86,690	1,170,315
20	1,196,461	95,717	1,292,178

Repeat problem 5 but assume a 7 percent return can be earned ?

Life insurance policy will be accumulated after 20 years to $21,28,326/- as indicated in Exhibit 3 and f rate of return is 7% instead of 6%, however if Studebaker will opt the suggestion of Morton, Studebaker will have to take loan further for $2,50,000/-, and that amount mortgage Loan will be repaid till the end of 30 years and balance of loan at the time of maturity of LIC (i.e. at the end of 20 years) would be $4,40,393.33/-.

Comer’s criticisms implied that the single-premium life insurance policy is an

unattractive investment for Studebaker. What do your previous answers suggest?

Yes Comer’s criticisms is correct that single investment policy is not an attractive investment for Studebaker as mentioned below:-

If Studebaker would have opted the Morton’s way of investment then in such case at the end of 20 years Studebaker would have to $1,763,925/-, with the increase in Loan Installment of $26145.31/- every year and loan balance of $440393.33/-, at the end of 20 years, accumulated balance of LIC according to increased return @ 7% would be $21,28,326/-

Calculation of the Discount Rate

And If with the same resources Studebaker would have invested $300,000 in a long-term asset yielding 8 percent for 20 years then accumulated balance in hands of Studebaker would be $1,398,287/- and if $26145.31/- would have been invested every year together with earlier invested sum at the rate of 8%, accumulated balance at the end of 20 years would be $1,292,178/-, if we take total of both of these Investments total accumulated with same resources would have been $26,90,465/-, due to increase in rate of return, the accumulated balance of these investments are more than the Morton’s suggestions by $9,26,540/-.

(26,90,465/- – 17,63,925/-).

Requirement at the end of 20 years		$3,500,000.00
Amount will be received out of the investment of $300000 at the end of 20 years as calculated in 6 (a)	$1,398,287.14
Balance Amount required at the end of 30 years		$2,101,712.86
End of Year	Long Term Assets Value at Opening of the year (Figures in $)	Return earned at the rateof 8% during the year (Figures in $)	Long Term Assets  Value at Closing of the year (Figures in $)
1	42,525.05	3,402.00	45,927.05
2	88,452.10	7,076.17	95,528.27
3	138,053.32	11,044.27	149,097.59
4	191,622.64	15,329.81	206,952.45
5	249,477.50	19,958.20	269,435.70
6	311,960.75	24,956.86	336,917.61
7	379,442.66	30,355.41	409,798.07
8	452,323.12	36,185.85	488,508.97
9	531,034.02	42,482.72	573,516.74
10	616,041.79	49,283.34	665,325.14
11	707,850.19	56,628.01	764,478.20
12	807,003.25	64,560.26	871,563.51
13	914,088.56	73,127.08	987,215.65
14	1,029,740.70	82,379.26	1,112,119.95
15	1,154,645.00	92,371.60	1,247,016.60
16	1,289,541.65	103,163.33	1,392,704.98
17	1,435,230.03	114,818.40	1,550,048.44
18	1,592,573.49	127,405.88	1,719,979.37
19	1,762,504.42	141,000.35	1,903,504.77
20	1,946,029.82	155,682.39	2,101,712.21

Hence $2101712/- will be received after 20 years by investing $42525.05/- every year.

Requirement at the end of 20 years		$3,500,000.00
Amount will be received out of the investment of $300000 at the end of 20 years as calculated in 6 (a)	$1,398,287.14
Balance Amount required at the end of 30 years		$2,101,712.86

End of Year	Long Term Assets Value at Opening of the year (Figures in $)	Return earned at the rateof 8% during the year (Figures in $)	Long Term Assets  Value at Closing of the year (Figures in $)
1	55,402.45	4,432.20	59,834.65
2	115,237.10	9,218.97	124,456.06
3	179,858.51	14,388.68	194,247.19
4	249,649.64	19,971.97	269,621.62
5	325,024.07	26,001.93	351,025.99
6	406,428.44	32,514.28	438,942.72
7	494,345.17	39,547.61	533,892.78
8	589,295.23	47,143.62	636,438.85
9	691,841.30	55,347.30	747,188.60
10	802,591.05	64,207.28	866,798.34
11	922,200.79	73,776.06	995,976.85
12	1,051,379.30	84,110.34	1,135,489.64
13	1,135,489.64	90,839.17	1,226,328.82
14	1,226,328.82	98,106.31	1,324,435.12
15	1,324,435.12	105,954.81	1,430,389.93
16	1,430,389.93	114,431.19	1,544,821.12
17	1,544,821.12	123,585.69	1,668,406.81
18	1,668,406.81	133,472.55	1,801,879.36
19	1,801,879.36	144,150.35	1,946,029.71
20	1,946,029.71	155,682.38	2,101,712.09

If Investment can be made only up to the end of 12 years in such case he has to invest $55402.45/- to receive $2101712/- at the end of 20 years.

$5,672.59/- will required to paid on monthly basis till 20 years for repayment of loan of $705,000/- which means yearly payment will be ($5,672.59/- * 12)  $68,071.08/-, however if we go for yearly installment basis then installment amount was $68,622/-

In case of Monthly payment system total of yearly installments is less in comparison with yearly payment system, reason behind is that in Monthly installment System interest is charged on less principal amount as payment is being made monthly and principal part is reducing monthly, and in case of yearly payment system, installment is paid at the end of the year and interest is charged on comparative large amount of principle (Wiley 2018).

Corner’s has calculated cost of $47,145.31/- for the first year, by taking total of interest of $21000/- on $3,00,000/- @ 7% interest and $26145.31/- as increased installment amount.

For 20^th year Corner has calculated $1,70,502.31/- as extra annual cost by taking total of following :-

Increase Installment amount of loan $26,145.31/-

Interest lost on $300000 in 20^th year $75,947/-

Interest lost on $26145.31 and its cumulative Investment in 20 years $68,410/-

End of Year	Long Term Assets Value at Opening of the year (Figures in $)	Return earned at the rate of 7% during the year (Figures in $)	Long Term Assets  Value at Closing of the year (Figures in $)	Long Term Assets Value at Opening of the year (Figures in $)	Return earned at the rate of 7% during the year (Figures in $)	Long Term Assets  Value at Closing of the year (Figures in $)	Total Cost of the year
1	300,000	21,000	321,000	26,145	1,830	27,975	47,145
Continued Calculation
18	947,645	66,335	1,013,980	888,915	62,224	951,139	148,923
19	1,013,980	70,979	1,084,958	977,285	68,410	1,045,695	159,348
20	1,084,958	75,947	1,160,905	1,071,840	75,029	1,146,869	170,502

Policy suggested by morton do not consider the opportunity cost of the amount required to be invested in life insurance policy, return in life insurance policy is 6% and return in other investment of markets are 7-8% per annum, hence in our opinion Morton’s policy do have various mistakes and do not provide most appropriate benefit. (James 2015)

In our Critical Evaluation we found that investment of funds in outside assets which are yielding 8% return per annum is better instead of life insurance policy, further it is not an good option to take loan at 9% rate of interest and invest that funds at 6% interest rate or an interest rate less than 9%, hence option given by Morton is not correct and in our opinion and only 300000 shall be invested in appropriate manner.

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