Time Value Of Money: Concepts And Applications In Economics And Finance

Concept of Time Value of Money

1. Fundamentals of Time Value Concept :

Time Value of money is widely used concept since long, we  use Time value of money in felid of economics and finance, such as in Capital budgeting, valuation of business, valuation of securities and many more.

As the name suggests basic approach of time value of money is that it is better to have the money today is present instead of having that same amount in future, as if one have that amount of money in his hands at present then one can invest it somewhere and can earn money by investing funds at present.

To make this clear in more better way we will explain it with an example ;

 If you have $1000 today in your hand and any way of investment at the rate of 10% per annum, you will have $1100 a year from now, and on the other hand a $1000 a year from now, at the same rate of 10 % per annum, are just $909 today (Woodruff 2018)

1. Discounting and compounding process and their uses

Time value of Money concept says that worth of a unit today will be changed in future, for putting it simply, the value of one dollar today will decrease in future, the entire concept s about the present value of money and future value of money

There are two ways of ascertaining the value of money at different point of time, one is compounding and another is discounting (Gardner 2017)

Compounding method is used to determine future value of present money.

Discounting method is used to determine present value of future money.

Both have different rates for calculation for compounding , compounding rate of interest is used and for discounting, discounting rate of interest is used.

 Compounding and discounting both helps in rational decision making, as compounding helps in determining the future value of present cash flow, and on the other hand discounting helps in determining the present value of future cash flows.

Discounting is rational process to use for making appropriate decisions in comparison with compounding reason being, in compounding we use rate of return of future which is not certain at present, which leads to inappropriate decision making, however on the other hand in discounting method we need to determine present value of future return, and rate used for discounting is known at present which gives more appropriate results for decision making (Keythman 2015)

For Compounding following formula is used:-

Compounding and Discounting Methods

FV =  PV (1 + R) ^ n

For Discounting following formula is used:-

PV =  FV / (1 + R) ^ n

1. Discount rate and main components of the discount rate

The term discount rate is most widely used fundamental term in finance in economics. Discount rate is used to determine present value of expected cash lows. These is an inverse relationship between present value and discount rate, higher the discount rate is used, lower will be the present value of cash flows, and lower the discount rate, higher will be the present value of cash flows.

As simple is to understand the concept of discount rate more difficult to determine appropriate discount rate, in determining the appropriate discount rate following must be Considered and assessed properly before determining any discount that that is to be used to discount future expected cash flows:

1. Pure Interest
2. Risk
3. Inflation
4. Reinvestment Risk
5. Variability of returns

We use different discount rates or evaluating different decisions based on the above mentioned factors, more the risk, more will be the discount rate and vise-versa, each and every point mentioned above will affects the discount rate, this will depend on case to case basis (Dalfard 2016)

Discount rate may be calculated by using following formula :

1. Use of time value in valuation of financial instruments such as bonds, equity and preference shares :-

Bonds, preference shares and equity shares are most common ways that are used while doing investment, to take appropriate decision as in which kind of securities investment must be made, it is necessary to determine value of these securities, there are many kinds of ways to determine value of these securities and Time value is widely used in valuation of Shares, Debentures, to determine value of these securities first one has to determine value of business,  In valuation of Business present value of cash flows for explicit period and present value of terminal value is calculated and added to arrive at Gross Value of the business. This value is for all funds providers, i.e. Debenture holders, Equity share holders and Preference shareholders.

Valuation is not only done to determine the most appropriate way of investment however valuation is a most crucial decision for a company to determine value of its securities like bond, debentures, Preference shares and equities, as all the holders of these securities are very much concerned with the value if their existing investment, hence every company would like to use most appropriate way of doing valuation of business and securities like bonds, debentures, Preference shares and equities, as no company would like to lose its current investors and potential investors. Discounted cash flow method of valuation is most trusted way for determining value of securities (Sanders 2017)

The Role of Discount Rate in Discounted Cash Flow Analysis

To arrive at the value of equity share holders under Firm approach of valuation, we can use following formula :-

Value of Equity holders = Present value of Cash flows for explicit period + Present Value of Terminal Value – Opening balance of loan as on Valuation date + Opening Surplus cash which is not considered for working capital requirement + realizable Value of Surplus assets etc.

1. Capital budgeting and time value:

Time Value of money is a very important part of capital budgeting, and it provide small business holders a base with the help of capital budgeting to take appropriate decisions, with the help of discounting and capital budgeting small business holders can adjust cash flows with the passage of time and this process is known as discounting to present value and allows preference to dollar received today over the dollar received tomorrow.

Time Value of Money is used in following concepts of capital budgeting :

1. Net Present Value (NPV)
2. Internal Rate of Return (IRR)
3. Total Cost Approach (TCA)
4. Project profitability Index (PPI)

1. Net Present Value (NPV):

Net present value is most used technique of capital budgeting, In net present value technique of Capital budgeting, time value of money is used to determining profitability of project, by discounting future expected cash flows and its terminal value. If the projects net present value is grater or equal to zero the project is acceptable.

NPV = Present value of future cash Inflows – Present Values of cash out flow (Freedman 2018)

1. Internal Rate of Return (IRR)

Internal rate of return is another most widely used technique of Capital budgeting,  The IRR method is applies in manner which is reverse of NPV method of capital budgeting technique, This Method tends to find out a discount rate, for undiscounted cash flows of the projects, in such a way resulting NPV of project to Zero, that Zero represents the BEP i.e. breakeven point of project profitability.

1. Total Cost Approach (TCA)

The TCS approach allows small business owners to evaluate multiple projects together at one time. In this Method, all cash inflows and outflows are adjusted to determine competing alternative. All the projects which gives positive NPV are acceptable, however the project with the greatest NPV is preferred and most profitable.

1. Project profitability Index (PPI)

Where there is a situation that funds available are limited, a small business owner can calculate profitability index to determine preferable project, by dividing NPV of project with the Investment made, this capital budgeting technique is known as PPI, higher PPI values imply more desirable project. (Wiley 2018)

There is always a biggest obstacle with time value of money is to determine discount rate or compound rate to be used to determine present value of cash flows, as discount rate and compound rates are dependent on various factors, and these factors changes form one business to other, thereby discount rate used for determining present value of cash flows may be different from discount rate used to determine present value of cash flows of any other business.

Application of Time Value of Money in Capital Budgeting Techniques

Same as discussed above applies to compounding rate, as it is also based on various factors, and those factors may be variable form one business to another, hence compound rate used for compounding cash flows of one business may be different for compounding cash flows of another business.

Hence to determine correct and appropriate discount rate is a critical matter.

Another issue with Time Value of Money is to determine future expected cash flows and there time of occurrence, as only expectation can be done, nothing can be said with certainty, and various fluctuation may come, these fluctuations may lead a decision based on TVM wrong.

The following goals Studebaker is focusing upon is the diversification of the business and buy and hold goal. Diversification is described as some technique where all the investment is not invested in one portfolio and it is allocated to different  baskets so that if one basket fails then the entire investment doesn’t fall out. Diversification helps in reducing the risk. It gives the portfolio in a non-risky position. It is a type of strategy which is a risk management technique which actually mixes different variety of investments in a portfolio. It actually strives to remove the unsystematic risk in a portfolio so that the positive investment outlast the negative ones and balances them. further change benefits can be expanded by investing in distant securities as they are less related to domestic investment. It is a good corporate strategy so that one can enter in to  new market and helps in managing risk.

The next strategy is buy and hold is opting for good profits and returns as compared to long run and not getting involved in day to day activities and one need to have good investment ways before the actual investment and also less attention is involved. In our opinion policy opted by Studebaker are helpful for him and goals are identified therefore which will help them in future.

1. In this LIC policy the sum that is invested will be increasing at a good rate with a return of around and it will automatically increase the investment overall which was there hence the sum will be calculated as below:

Year	Life Insurance value at beginning (Figures in $)	Return of 6 % that is earned (Figures in $)	LIC policy value at the end (Figures in $)
1	550,000	33,000	583000
2	583,000	34,980	617980
3	617,980	37,079	655,059
4	655,059	39,305	694,3624
5	694,364	41,662	736,025
6	736,025	44,162	780,186
7	780,186	46,812	826,998
8	826,998	49,620	876,618
9	876,618	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	1106,709
13	1,106,709	66,403	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	1,481,029
18	1,481,029	88,864	1,569,890
19	1,569,890	94,195	1,664,085
20	1,664,085	99,847	1,763,930

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

Installment formula is as follows:-

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

Installment  = [450000 * 9% * ( 1 + 0.09 )^20] / [ ( 1 + 0.09 )^20 – 1 ]

The amount of investment is  $77230.26. (WordPandit 2018)

Year	Beginning balance ( $)	Installment figure ( $)	Payment of Interest ( $)	Repayment of the Principal Amount($) (Figures in $)	Ending balance ( $)
1	705000.00	77230.26	63450.00	13780.26	691219.75
2	691219.75	77230.27	62209.78	15020.49	676199.26
3	676199.26	77230.26	60857.93	16372.33	659826.93
4	659826.93	77230.26	59384.42	17845.84	641981.10
5	641981.10	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	49772.20	27458.03	525566.73
10	525566.73	77230.25	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	38471.00	38759.27	388696.40
14	388696.40	77230.25	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	6376.85	70853.44	0.29

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

Challenges with Time Value of Money

and 20?

Answer :- 19^th year end balance will be $466986.70 and 20 the will be $440393.35, which is calculated as follows : 

Amortization Amount  705000 /-  9  % Mortgage Rate and the loan id for 30 Years.
Year end	Beginning balance ( $)	Installment Amount(Figures in $)	Interest Payment (Figures in $)	Principle Repayment (Figures in $)	Ending Balance (Figures in $)
1	705000.00	68622	63450.00	5172.13	699827.87
2	699827.87	68622	62984.52	5637.62	694190.25
3	694190.25	68622	62477.13	6145.00	688045.25
4	688045.25	68622	61924.08	6698.06	681347.19
5	681347.19	68622	61321.26	7300.88	674046.31
6	674046.32	68622	60664.17	7957.96	666088.35
7	666088.35	68622	59947.95	8674.18	657414.18
8	657414.19	68622	59167.28	9454.85	647959.33
9	647959.33	68622	58316.34	10305.79	637653.54
10	637653.54	68622	57388.83	11233.32	626420.23
11	626420.23	68622	56377.82	12244.31	614175.92
12	614175.92	68622	55275.84	13346.29	600829.63
13	600829.63	68622	54074.68	14547.46	586282.16
14	586282.16	68622	52765.39	15856.74	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	46239.07	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 specifies that $1,763,925 will be collected after 20 years in the life

insurance policy. Is this true?

Answer :-

It is correct and the LIC policy will be getting accumulated after

Years to 1763926 as shown in the exhibit 3 and also it is calculated in answer of the 1^st Question. And if Studebaker will be opting the suggestions of Morton Studebaker will be taking a loan of $250000 and the loan will be repaid at the end of 30 year . The balance of loan at the maturity time (after 20 year ) 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 getting accumulated after 20 Years. Following are the calculations:-

End of Year	Long Term Assets Value at Opening of the year ($)	Return earned at 8%  ( $)	Long Term Assets  Value (closing)($)
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 ?

$1,292,179 is getting accumulated after 20 Years, if Studebaker Invests $26145.31/- each year collected will the investment made earlier. 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 ?

A further loan of $2,50,000 shall be required for opting the suggestion of Morton which will require a total of thirty years to repay the loan in full . However, the life insurance policy will accumulate an amount of $21,28,328 with a return of 7% as suggested in Exhibit 3 and where the suggestion of Morton is accepted, the amount LIC on maturity will amount to $4,40,396.45.

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 (Tonagatti 2017)

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

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

All the Comer’s criticisms is very correct that the single investment policy does not prove to be attractive investment for Studebaker which is calculated:

Studebaker’s Goals for Business Diversification and Buy and Hold Strategy

Studebaker if he has adopted the Morton;s way in the investment field than at the end of 20 years Studebaker will have to invest $1763925 and it will increase the loan installment of $26145.31 each and every yearand the balance of the loan is $440393.33 and at the end the balance that @7 percent will be $2128326.

Woth the same resources the inidivual could have invested $ 300000 in a asset which is long term which yields 8 percent for 20 year and also the accumulated balance will be $1,398,287 and also and if $26145.31/- is being invested each year together and also with the invested sum @ 8%, accumulated balance at the end of 20 years would be $1,292,178/-, and after taking total of both of the Investments the total collected with same incomes is  $26,90,465/-, as the rate of return has been incraesed, the accumulated weighing scale of the investments are greater than Morton’s proposals by $9,26,540/-.

(a) Answer :-

Requirement at end of 20 years		$3,500,000.00
Amount which will be getting received out of the investment of $300000 in end of  20 years as calculated in 6 (a)	$1,398,287
Balance Amount which is required at the end of 30 years		$2,101,712
	End of Year	Long Term Assets Value at Original /Beginning year ($)	Return @8 percent ($)	Long Term Assets  Value at ending($)
	1	42,525.05	3,402.00	45,927.05
	2	88,452.10	7,076.18	95,528.28
	3	138,053.3	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	871,563.52
	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

 $2101712/- will be received after 20 years by capitalizing $42525.05/- each year.

1. (B) Answer :-

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 (Beginning) ($)	Return earned at the rateof 8% ($)	Long Term Assets  Value at the end ($)
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 only 12 years investment is done he has to invest  $55402.45/- to receive $2101712/ at the end.

$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, and the reason is that in  Monthly installment System interest is being allocated on less principal amount as the payment iare being made monthly and main part is reducing monthly which is also in case of yearly payment system, installment is given at end of the year and also the interest is granted on proportional large sum of principle.

The calculation of Corner which has a cost of $ 47145 is for the 1^st year and the total interest of $21000 on the amount of $30000 at the rate of 7 percent and also 26145$ as the installment amount which has been increased

In20^th year Corner has designed $1,70,502- as an extra twelve-monthly cost

Increase Installment number of loan $26,145.31/-

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

Interest which has been lost on $26145.31 with the cumulative Investment 20 years which is $68,410/-

Calculation of above is mentioned below:-

($)

End of Year	Long Term Assets Value at Opening of the year	Return earned at the rate of 7% during the year	Long Term Assets  Worth at the end	Long Term Assets Worth at Opening of the year	Return earned @ of 7% during the year	Long Term Assets  at closing	Total cost which is incurred
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

The policy which was suggested by Morton don’t consider the oppurtuinity  costs that is the amount that is required to be invested in the Life Insurance Policy which was 6 percent and also the market rate was 7 to 8 percent then it can be concluded that thenpolicy of Morton contain enough misakes and don’t provide good benefit to the users. (Bahner 2007)

It was found in the critical evalution it is found that the investment of all the funds in the external assets which posses a return of 8 percent per annum is portrayed better as compared to the Lifeinsurance Policy and also it is not feasible to take loan at the rate of 9 percent rate of interest and then invest that for 6 percent as the return will be low hence the Morton option is incorrect  and thus only 300000 investment should be made.

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