Exercise 10-5A
a.
Present valuePresent value / = / Future value / x / table factor / = / Present value
Present value / = / $16,000 / x / 2.913712* / = / $46,619.39
Present value / = / $24,000 / x / 0.592080** / = / 14,209.92
Total present value / = / 60,829.31
Cost of vans / = / (52,000.00)
Net present value / = / $8,829.31
*Table 2, n= 4, r=14%
**Table 1, n= 4, r=14%
b.Since the net present value is positive, the investment opportunity can be expected to earn a rate of return that is greater than the cost of capital. The analysis suggests that the investment opportunity should be accepted.
Exercise 10-9A
a.Determination of the annuity table values can be accomplished by dividing the cost of the investment by the annuity:
First investment: $9,335.16 ÷ $2,400 = 3.88965. Locating this value in Table 2 indicates that the investment is expected to earn an internal rate of return of 9%.
Second investment: $6,217.13 ÷ $2,500 = 2.486852. Locating this value in Table 2 indicates that the investment is expected to earn an internal rate of return of 10%.
b.Since the second investment has a higher internal rate of return it should be accepted.
c.Many other factors should be considered. Some of these are: (1) The life of the investments. The second investment has a three-year useful life. If the company is unable to reinvest funds at greater than 9% at the end of three years, its effective rate of return for the second investment could fall below the return generated by the first investment. (2) The size of the investment. If the company has $9,335.16 (i.e., amount of the first investment opportunity) of funds available to invest and only invests $6,217.13 (i.e., amount of the second investment opportunity), then $3,118.03 ($9,335.16 $6,217.13) of uninvested funds will exist. If these funds are not invested at a rate greater than 9%, the overall return from the residual funds and the second investment could fall below 9%. (3) Confidence in the accuracy of projected cash flows. Uncertainty is just another word for risk. If the projections for one investment are less certain than the other, this risk factor should be considered in the final decision.
Exercise 10-12A
a.
Cash cost of investment Annual cash inflow = Payback period
Alternative 1
$1,800,000 $600,000 = 3 years
Alternative 2
$3,600,000 $900,000 = 4 years
Since the payback period for the first airplane is shorter, Alternative 1 should be accepted based on the payback approach.
b.The payback method does not consider the life of the investment. In this case, Alternative 1 provides the quickest payback but Alternative 2 continues to provide cash inflows for three years after Alternative 1 has expired. Also, payback does not consider the time value of money.
Exercise 10-13A
a.
Year / Nature of Item / Cash Flows2008 / Revenue / $10,000
2009 / Revenue / 10,000
2010 / Revenue / 7,000
2010 / Major overhaul / (3,000)
Total / $24,000
The payback occurs at the end of 3 years.
b.Average cash inflow is computed as follows:
($10,000+$10,000+$7,000$3,000+$6,000+$4,800+$3,200) ÷ 5 = $7,600per year
Payback period = $24,000 ÷ $7,600 = 3.2years
Problem 10-16A
a.
Alternative 1
Cash Inflows
/ Table Value / Present ValueAnnual cash inflows
/ $280,000 / x / 2.7981811 / = / $783,490.68Salvage value / 100,000 / x / 0.5522912 / = / 55,229.10
Working capital recovery / 40,000 / x / 0.5522912 / = / 22,091.64
Cash outflows
Cost of vans
/ (720,000.00)Working capital increase / (40,000.00)
Net present value / $100,811.42
1Table 2, n= 4, r = 16%2Table 1, n= 4, r = 16%
Alternative 2Cash Inflows / Table Value / Present Value
Year 1
/ $160,000 / x / 0.8620691 / = / $137,931.04Year 2 / 320,000 / x / 0.7431632 / = / 237,812.16
Year 3 / 400,000 / x / 0.6406583 / = / 256,263.20
Year 4 / 440,000 / x / 0.5522914 / = / 243,008.04
Salvage value / 80,000 / x / 0.5522914 / = / 44,183.28
Cash outflows
Cost of trucks
/ (800,000.00)Training cost / (16,000.00)
Net present value / $103,197.72
1Table 1, n=1, r=16%3Table 1, n=3, r=16%
2Table 1, n=2, r=16%4Table 1, n=4, r=16%
b.
Alternative 1:Present value of cash inflows / $860,811.42
–––––––––––––––––––––––––––––––– / = / –––––––––––––– / = / 1.133
Present value of cash outflows / $760,000
Alternative 2
Present value of cash inflows / $919,197.72
–––––––––––––––––––––––––––––––– / = / –––––––––––– / = / 1.126
Present value of cash outflows / $816,000
c.Alternative 1 will provide the higher rate of return, but alternative 2 results in a greater net present value. With Alternative 1 there is only $760,000 invested while there is $816,000 invested with Alternative 2. If additional funds can be invested at the rate of return provided by Alternative 1, then that alternative should be accepted. However, if the additional $56,000 of capital (i.e., $816,000 – $760,000) must sit idle, then Alternative 2 may be the better option if Special Delivery actually has that much money. The information provided is insufficient to determine which the better alternative is.
Problem 10-21A
a.
Cash Inflows
/ Table Value* / Present ValueYear 1
/ $42,000 / x / 0.892857 / = / $37,499.99Year 2 / 48,000 / x / 0.797194 / = / 38,265.31
Year 3 / 60,000 / x / 0.711780 / = / 42,706.80
Year 4 / 92,000 / x / 0.635518 / = / 58,467.66
Cash outflows
Cost of investment
/ (200,000.00)Net present value / $(23,060.24)
*Table 1, n = 1 - 4, r=12%
Since the net present value of the project is negative, Mr. Harper should not approve the project.
b. & c. The cash flow should increase by $12,000 per year (i.e. $40,000 x 30%) due to the tax deduction on depreciation.
The revised cash flow forecast and the net present value computation should be as follows:
Cash Inflows / Table Value / Present ValueYear 1
/ $ 54,000 / x / 0.892857 / = / $ 48,214.28Year 2 / 60,000 / x / 0.797194 / = / 47,831.64
Year 3 / 72,000 / x / 0.711780 / = / 51,248.16
Year 4 / 104,000 / x / 0.635518 / = / 66,093.87
Cash outflows
Cost of investment
/ (200,000.00)Net present value / $ 13,387.95
Since the net present value with the revised cash flow is positive, Mr. Harper should approve the project.