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 perpetuity starting in year 8 would be worth roughly $5.  The difference between these cash flows is therefore approximately $5.  PV = 10 – 5= $5 (approximately)

d.        PV = C/(r-g) = 10,000/(.10-.05) = $200,000.

9.       a.    PV = 10,000/(1.05⁵) = $7,835.26 (assuming the cost of the car does not     

appreciate over those five years).

b.        You need to set aside (12,000 × 6-year annuity factor) = 12,000 × 4.623 =

           $55,476.

c.        At the end of 6 years you would have 1.086 × (60,476 - 55,476) = $7,934.

10.       a.    FV = 1,000e^.12x5 = 1,000e^.6 = $1,822.12.

      b.     PV = 5e-.12 x 8 = 5e-.96 = $1.914 million

      c.     PV = C (1/r – 1/re^rt) = 2,000(1/.12 – 1/.12e ^{.12 x15}) = $13,912