|
Net profit of Fisher Ltd for year 2017-18 |
$ 800,000 |
|
Bradley Lane’s Share |
12% |
|
Dividend payout ratio |
70% |
|
Growth rate in earnings |
20% |
|
Estimated profit of Fisher Ltd for year 2018-19 (800000 x (1 + 20%)) |
$ 960,000 |
|
Dividend to be received in late September 2018 by Bradley Lane (800000 x 12% x 70%) |
$ 67,200 |
|
Dividend to be received in September 2019 by Bradley Lane (960000 x 12% x 70%) |
$ 80,640 |
|
Amount required in late September 2019 |
$ 95,000 |
|
Amount to be received in late September 2019 from Dividend |
$ 80,640 |
|
Balance amount required |
$ 14,360 |
|
Interest rate |
10% |
Dividend Payout Ratio
Amount which can be consumed by Bradley Lane in late September 2018
= 67200 – (14360/ (1+ 10%))
= $54,145
Discount rate = 6%
Cost of Van A = $70,000
Useful life (in years) = 3
Operating cost per annum = $7,000
Present value factor for 3 years at 6% = 2.6730
Annual Equivalent cost for Van A = (70000 / 2.6730) + 7000
= $33,188
Cost of Van B = $90,000
Useful life (in years) = 4
Operating cost per annum = $9,000
Present value factor for 4 years at 6% = 3.4651
Annual Equivalent cost for Van B = 90000 / 3.4651 + 9000
= $34,973
Van A should be selected as annual equivalent cost for Van A is less than annual equivalent cost for Van B.
Face value of Notes = $1,000
Coupon rate per annum = 13%
Interest amount = 1000 x 13%
= $130
Required rate of return = 19%
Payment schedule after meeting
|
Particulars |
Date |
Year |
Payment Amount |
Present Value Factor |
Present Value |
|
Sep-19 |
1 |
$ – |
0.8403 |
$ – |
|
|
Sep-20 |
2 |
$ – |
0.7062 |
$ – |
|
|
Interest due on Sep-21 paid in Sep-21 |
Sep-21 |
3 |
$ 130 |
0.5934 |
$ 77 |
|
Interest due on Sep-22 paid in Sep-22 |
Sep-22 |
4 |
$ 130 |
0.4987 |
$ 65 |
|
Interest due on Sep-23 paid in Sep-23 |
Sep-23 |
5 |
$ 130 |
0.4190 |
$ 54 |
|
Interest due on Sep-19 paid in Sep-23 |
Sep-23 |
5 |
$ 130 |
0.4190 |
$ 54 |
|
Interest due on Sep-20 paid in Sep-23 |
Sep-23 |
5 |
$ 130 |
0.4190 |
$ 54 |
|
Repayment of Notes |
Sep-23 |
5 |
$ 1,000 |
0.4190 |
$ 419 |
|
$ 724 |
Current value of each Farmers Bank unsecured note = $724
|
Age today (in years) |
42 |
|
Retirement age (in years) |
63 |
|
Period of investment (in years) |
21 |
|
Period of investment (in months) (21 x 12) |
252 |
|
Contribution each month |
$ 3,700 |
|
Targeted sum |
$ 1,600,000 |
|
Rate of interest per annum compounding monthly |
4.80% |
|
Monthly interest rate (4.80% / 12) |
0.40% |
Fund value at retirement = (3700 / 0.40%) ((1 + 0.40%)^(252) – 1)
= (925000) x (1.73461)
= $1,604,515.59
= $1,604,516
Ruth Bray will have $1,604,516 at the age of retirement.
Yes, she will achieve the targeted sum.
She will have surplus = 1604516 – 1600000
= $4,516
|
63 |
|
|
Pension required till (in years) |
87 |
|
Period of pension (in years) |
24 |
|
Period of pension (in months) (24 x 12) |
288 |
|
Rate of interest per annum compounding monthly |
4.80% |
|
Monthly interest rate (4.80% / 12) |
0.40% |
Suppose the monthly pension amount be M.
(M / 0.40%)(1 – (1 + 0.40%)^(-288)) = $1,604,516
M (170.8172) = $1,604,516
M = 1604516 / 170.8172
M = $9,393
Monthly pension Joan will receive is $9,393.
Interest rate per annum compounding monthly = 4.50%
Monthly interest rate (4.50% / 12) = 0.375%
Effective annual interest rate = (1 + 0.375%)^12 – 1
= 4.594%
|
4.50% |
|
|
Monthly interest rate (4.50% / 12) |
0.375% |
|
Repayment period (in years) |
25 |
|
Repayment period (in months) (25 x 12) |
300 |
|
Amount of loan |
$ 750,000 |
Suppose month instalment size be M.
(M / 0.375%)(1 – (1 + 0.375%)^(-300)) = $750,000
M (179.9103) = $750,000
M = 750000 / 179.9103
M = $4,169
Amount of monthly repayment is $4,169.
|
Interest rate per annum compounding monthly |
4.50% |
|
Monthly interest rate (4.50% / 12) |
0.375% |
|
Repayment period (in years) |
25 |
|
Repayment period (in months) (25 x 12) |
300 |
|
Amount of loan |
$ 750,000 |
Future value of repayment of $3000 per month = (3000 / 0.375%)((1 + 0.375%)^(12) – 1)
= $36,751.86
Loan pending at the end of year 1 = 750000 (1 + 0.375%)^12 – 36,751.86
= $747,703.01
Future value of repayment of $3500 per month = (3500 / 0.375%)((1 + 0.375%)^(12) – 1)
= $42,877.17
Loan pending at the end of year 2 = 747703.01 (1 + 0.375%)^12 – 42877.17
= $739,175.19
Suppose month instalment size be M after two years.
(M / 0.375%)(1 – (1 + 0.375%)^(-23M12)) = $739,175.19
M (171.756) = $739,175.19
M = 739175.19 / 171.756
Z = $4,303.64
M is $4303.64 per month.
Monthly repayment = $4,400
Suppose loan is repaid in n months.
$750,000 = (4400 / 0.375%) (1 – (1 + 0.375%)^(-n))
$750,000 = (1173333.33) (1 – (1 + 0.375%)^(-n))
750000 / (1173333.33) = (1 – (1 + 0.375%)^(-n))
0.6392 = (1 – (1 + 0.375%)^(-n))
(1 + 0.375%)^(-n) = 1 – 0.6392
(1.00375)^(-n) = 0.3608
Taking log on both sides
(-n) log 1.00375 = log 0.3608
(-n) 0.00162555828 = -0.442733471
(n) 0.00162555828 = 0.442733471
n = 0.44273347113 / 0.00162555828
n = 272.3577964
n = 272.36
Total months taken for loan repayment is 273 months (22 years 9 months).
|
Year |
Investment P ($) |
|
|
Cash flows |
Cumulative Cash Flows |
|
|
0 |
– 60,000 |
– 60,000 |
|
1 |
20,000 |
– 40,000 |
|
2 |
30,000 |
– 10,000 |
|
3 |
44,000 |
34,000 |
|
34,000 |
Payback period (Investment P) = 2 + (10000/ 44000)
= 2.23 years
|
Year |
Investment Q ($) |
|
|
Cash flows |
Cumulative Cash Flows |
|
|
0 |
– 60,000 |
– 60,000 |
|
1 |
30,000 |
– 30,000 |
|
2 |
30,000 |
– |
|
3 |
30,000 |
30,000 |
|
30,000 |
Payback period (Investment Q) = 2.00 years
On this basis, we should prefer Investment Q as its payback period is less than that of Investment P.
Payback period will be different in this case.
|
Year |
Investment P ($) |
|
|
Cash flows |
Cumulative Cash Flows |
|
|
0 |
– 60,000 |
– 60,000 |
|
1 |
20,000 |
– 40,000 |
|
2 |
30,000 |
– 10,000 |
|
3 |
44,000 |
34,000 |
|
34,000 |
Payback period (Investment P) = 3.00 years
|
Year |
Investment Q ($) |
|
|
Cash flows |
Cumulative Cash Flows |
|
|
0 |
– 60,000 |
– 60,000 |
|
1 |
30,000 |
– 30,000 |
|
2 |
30,000 |
– |
|
3 |
30,000 |
30,000 |
|
30,000 |
Payback period (Investment Q) = 2.00 years
Required rate of return = 8%
|
Year |
PVF |
Investment P ($) |
|
|
Cash flows |
Present Value |
||
|
0 |
1.0000 |
– 60,000 |
– 60,000 |
|
1 |
0.9259 |
20,000 |
18,519 |
|
2 |
0.8573 |
30,000 |
25,720 |
|
3 |
0.7938 |
44,000 |
34,929 |
|
34,000 |
19,167 |
NPV of Investment P = $19,167.30
Profitability Index of Investment P = (18519+25720+34929) / 60000
= 1.32
|
Year |
PVF |
Investment Q ($) |
|
|
Cash flows |
Present Value |
||
|
0 |
1.0000 |
– 60,000 |
– 60,000 |
|
1 |
0.9259 |
30,000 |
27,778 |
|
2 |
0.8573 |
30,000 |
25,720 |
|
3 |
0.7938 |
30,000 |
23,815 |
|
30,000 |
17,313 |
NPV of Investment Q = $17,312.91
Profitability Index of Investment Q = (27778 + 25720 + 23815) / 60000
= 1.29
An estimate of IRR can be made using NPV profiling of both the investments.
NPV profiling for Investment P
|
Cost of capital |
NPV |
|
8.00% |
19,167 |
|
20.00% |
2,963 |
|
21.00% |
1,856 |
|
22.00% |
780 |
|
23.00% |
– 265 |
|
24.00% |
– 1,283 |
|
25.00% |
– 2,272 |
|
26.00% |
– 3,235 |
IRR (as whole number) = 23%
NPV profiling for Investment Q
|
Cost of capital |
NPV |
|
8.00% |
17,313 |
|
20.00% |
3,194 |
|
21.00% |
2,218 |
|
22.00% |
1,267 |
|
23.00% |
341 |
|
24.00% |
– 561 |
|
25.00% |
– 1,440 |
|
26.00% |
– 2,297 |
IRR (1 decimal number) = 23.4%
Crossover rate is that rate of return at which both projects produce equal NPV. It is calculated using IRR of differences of cash flows of both the projects.
|
Year |
Cash Flows |
||
|
Investment P ($) |
Investment Q ($) |
Differences |
|
|
0 |
– 60,000 |
– 60,000 |
– |
|
1 |
20,000 |
30,000 |
– 10,000 |
|
2 |
30,000 |
30,000 |
– |
|
3 |
44,000 |
30,000 |
14,000 |
|
34,000 |
30,000 |
Crossover rate (IRR of Differences) = 18.32%
Summary of results
|
Criteria |
Payback period |
NPV |
PI |
IRR |
|
Investment P |
2.23 |
$19,167.30 |
1.32 |
22.75% |
|
Investment Q |
2.00 |
$17,312.91 |
1.29 |
23.38% |
The main objective of any organization is to maximize shareholders’ wealth.
Payback period – As per payback period criteria, Project Q should be selected as Project Q has lower payback period.
NPV (Net Present Value) – As per NPV criteria – Project P should be selected as Project P has higher NPV.
PI (Profitability Index) – As per Profitability Index criteria – Project P should be select as Project P has higher PI.
IRR (Internal Rate of Return) – As per IRR criteria, Project Q should be selected as Project Q has higher IRR.
NPV is preferred over payback period because:
- Payback period ignores time value of money and cash flows occurring after payback period.
- It ignores time value of money.
NPV will be preferred over the payback period and IRR because assumption of IRR that returns will be reinvestment at the rate equal to IRR is not true in real world.
Generally NPV and PI both give same results.
Due to above reasons, we accept the recommendation of NPV and project P should be selected.
|
Cost of each hydrofoils |
$ 480,000 |
|
Total cost of hydrofoils (480000 x 2) |
$ 960,000 |
|
Tax rate |
30% |
|
Cost of capital |
11% |
|
Savings in energy and labour costs |
$ 160,000 |
|
Useful life of new hydrofoils (in years) |
4 |
|
Depreciation on each hydrofoils (480000 / 4) |
$ 120,000 |
|
Depreciation for both the hydrofoils (120000 x 2) |
$ 240,000 |
|
Salvage value of each new hydrofoils |
$ 75,000 |
|
Salvage value for both the hydrofoils (75000 x 2) |
$ 150,000 |
|
Tax deductible expenses in year 2 |
$ 30,000 |
|
Tax deductible expenses in year 3 |
$ 40,000 |
|
Working capital requirement |
$ 30,000 |
|
WDV of old 3 hydrofoils (300000 x 3 x (4/6)) |
$ 600,000 |
|
Sale value of old 3 hydrofoils |
$ 510,000 |
|
Year |
0 |
1 |
2 |
3 |
4 |
|
Savings in energy and labour costs |
$ 160,000 |
$ 160,000 |
$ 160,000 |
$ 160,000 |
|
|
Depreciation |
-$ 240,000 |
-$ 240,000 |
-$ 240,000 |
-$ 240,000 |
|
|
Overhauling expenses |
-$ 30,000 |
-$ 40,000 |
|||
|
-$ 80,000 |
-$ 110,000 |
-$ 120,000 |
-$ 80,000 |
||
|
Tax savings |
$ 24,000 |
$ 33,000 |
$ 36,000 |
$ 24,000 |
|
|
-$ 56,000 |
-$ 77,000 |
-$ 84,000 |
-$ 56,000 |
||
|
Depreciation |
$ 240,000 |
$ 240,000 |
$ 240,000 |
$ 240,000 |
|
|
Cash flow from operations |
$ 184,000 |
$ 163,000 |
$ 156,000 |
$ 184,000 |
|
|
Working capital requirement |
-$ 30,000 |
$ 30,000 |
|||
|
Initial investment |
-$ 960,000 |
||||
|
Sale value of old hydrofoils |
$ 510,000 |
||||
|
WDV of old hydrofoils |
-$ 600,000 |
||||
|
Loss on sale |
-$ 90,000 |
||||
|
Tax savings |
$ 27,000 |
||||
|
Cash flow from sale of old hydrofoils |
$ 537,000 |
||||
|
Sale value of new hydrofoils |
$ 150,000 |
||||
|
WDV of new hydrofoils |
$ – |
||||
|
Profit on sale |
$ 150,000 |
||||
|
Tax |
-$ 45,000 |
||||
|
Terminal cash flow from new hydrofoils |
$ 105,000 |
||||
|
Total cash flows |
-$ 453,000 |
$ 184,000 |
$ 163,000 |
$ 156,000 |
$ 319,000 |
|
Present value factor |
1.0000 |
0.9009 |
0.8116 |
0.7312 |
0.6587 |
|
Present value |
-$ 453,000 |
$ 165,766 |
$ 132,294 |
$ 114,066 |
$ 210,135 |
Net Present Value = $169,261
Company should buy new hydrofoils as Net Present Value (NPV) is positive.
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