1. a. NPVA = –$36 + [$20 annuity factor (10%, 3 periods)]
b. Project A has the higher profitability index, as shown in the table below:
Project PV of
Cash Flow Investment NPV Profitability
Index
A
$49.74
$36
$13.74
0.38
B $62.17 $50 $12.17 0.24
c. A firm with a limited amount of funds available should choose Project A since it
2. a. The present value of the savings is $1,000/r.
r = 0.08 PV = $12,500 and NPV = –$10,000 + $12,500 = $2,500
b. IRR = 0.10 = 10%
c. Payback period = 10 years
3. a. Payback period = $2,500/$600 = 4.167 years
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b.
r = 2% NPV = $2,500 + [$600 annuity factor (2%, 6 years)]
4. We know that the undiscounted project cash flows sum to the initial investment because
payback equals project life. Therefore, the discounted cash flows are less than the initial
5. a.
Project Payback
A
3 years
b. Only Project B satisfies the 2-year payback criterion.
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Education.
55.404,2$
)10.1(
000,5$
)10.1(
000,3$
)10.1(
000,1$
10.1
000,1$
000,5$NPV
432
C
6.
a.
058,61$
08.1
)50.4$400,2(500,1
…
08.1
)50.4$400,2(500,1
08.1
)50.4$400,2(500,1
08.1
)00.4$400,2(500,1
08.1
)50.3$400,2(500,1
000,27$NPV
2043
2
8-?
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Education.
058,88$
08.1
)50.4$400,2(500,1
…
08.1
)50.4$400,2(500,1
08.1
)00.4$400,2(500,1
08.1
)50.3$400,2(500,1
PV
203
2
The equivalent annual annuity for this present value at 8% for 20 years is $8,968.92.
EAA = present value of annual savings/annuity factor (8%, 20 years)
= $88,058/9.8181 = $8,968.92
f. The difference between equivalent annual savings and costs is $6,219 ($8,969 –
$2,750). This value is equivalent to an annual annuity with a present value of
$61,058, the net present value from part (a).
$6,219 × annuity factor (8%, 20 years) = $6,219 × 9.8181 = $61,058
Est time: 16–20
Capital budgeting
7. a. NPVA =
43.43$
)02.1(
70$
)02.1(
50$
02.1
30$
100$
32
b. NPVA =
47.16$
)12.1(
70$
)12.1(
50$
12.1
30$
100$
32
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Education.
8. PV of costs = $10,000 + [$20,000 annuity factor (10%, 5 years)]
9. Leasing is the better option.
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Education.
10. a. Econo-cool costs $300 and lasts for 5 years. The annual rental fee with the same PV
b. Luxury Air is more cost-effective. It has the lower equivalent annual cost.
c. The real interest rate is now (1.21/1.10) – 1 = 0.10 = 10%
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11.
Time until
Purchase Cost NPV at
Purchase Date a NPV Today b
0
$400.00
$ 31.33
$ 31.33
1 320.00 48.67 44.25
12. The equivalent annual cost of the new machine is the 4-year annuity with present value
equal to $20,000:
000,20$
)15.1(15.0
1
15.0
1
4
C
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Education.
13. For harvesting lumber, the NPV-maximizing rule is to cut the tree when its growth rate
equals the discount rate. When the tree is young and the growth rate exceeds the discount
14. a. The equivalent annual cost (EAC) of the new machine over its 10-year life is found
by solving as follows:
000,20$
)04.1(04.0
1
04.0
1
10
C
b. If r = 12%, then the equivalent annual cost (EAC) is computed as follows:
000,20$
)12.1(12.0
1
12.0
1
10
C
8-?
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Education.