principle of corporate finance solution Essay

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CHAPTER 2
How to Calculate Present Values

Answers to Problem Sets

1. If the discount factor is .507, then .507*1.126 = $1

2. 125/139 = .899

3. PV = 374/(1.09)9 = 172.20

4. PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1,003

5. FV = 100*1.158 = $305.90

6. NPV = -1,548 + 138/.09 = -14.67 (cost today plus the present value of the perpetuity) 7. PV = 4/(.14-.04) = $40

8. a. PV = 1/.10 = $10

b. Since the perpetuity will be worth $10 in year 7, and since that is roughly double the present value, the approximate PV equals $5. PV = (1 / .10)/(1.10)7 = 10/2= $5 (approximately)

c. A perpetuity paying $1 starting now would be worth $10, whereas a
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From this equation, we can solve for the amount to be put aside each year.
PV(boat) = $20,000/(1.10)5 = $12,418
PV(savings) = Annual savings
Because PV(savings) must equal PV(boat):
Annual savings
Annual savings
Another approach is to use the future value of an annuity formula:

Annual savings = $ 3,276

22. The fact that Kangaroo Autos is offering “free credit” tells us what the cash payments are; it does not change the fact that money has time value. A 10% annual rate of interest is equivalent to a monthly rate of 0.83%: rmonthly = rannual /12 = 0.10/12 = 0.0083 = 0.83%
The present value of the payments to Kangaroo Autos is:

A car from Turtle Motors costs $9,000 cash. Therefore, Kangaroo Autos offers the better deal, i.e., the lower present value of cost.

23. The NPVs are: at 5% at 10% at 15%
The figure below shows that the project has zero NPV at about 11%.
As a check, NPV at 11% is:

24. a. This is the usual perpetuity, and hence:

b. This is worth the PV of stream (a) plus the immediate payment of $100:
PV = $100 + $1,428.57 = $1,528.57

c. The continuously compounded equivalent to a 7% annually compounded rate is approximately 6.77%, because: e0.0677 = 1.0700
Thus:

Note that the pattern of payments in part (b) is more valuable than the pattern of payments in part (c). It is preferable to receive cash flows at the start of every year than to spread the
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