Fin 814 Ch 2 - How to Calculate Present Values

CHAPTER 2

How to Calculate Present Values

Answers to Problem Sets

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

Est time: 01-05

1. DF x 139 = 125. Therefore, DF =125/139 = .899.

Est time: 01-05

1.       PV = 374/(1.09)9 = 172.20.

Est time: 01-05

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

Est time: 01-05

1. FV = 100 x 1.158 = $305.90.

Est time: 01-05

1.      NPV = −1,548 + 138/.09 = −14.67 (cost today plus the present value of the

perpetuity).

Est time: 01-05

1. PV = 4/(.14 − .04) = $40.

Est time: 01-05

1. a.          PV = 1/.10 = $10.

1.      Since the perpetuity will be worth $10 in year 7, and since that is roughly

double the present value, the approximate PV equals $5.

You must take the present value of years 1–7 and subtract from the total present value of the perpetuity:

        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).

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

Est time: 06-10

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

appreciate over those five years).

1. The six-year annuity factor [(1/0.08) – 1/(0.08 x  (1+.08)6)] = 4.623. You need to set aside (12,000 × six-year annuity factor) = 12,000 × 4.623 = $55,475.

1. At the end of six years you would have 1.086 × (60,476 - 55,475) = $7,935.

Est time: 06-10

10.        a.          FV = 1,000e.12 x 5 = 1,000e.6 = $1,822.12.

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

        c.         PV = C (1/r – 1/rert) = 2,000(1/.12 – 1/.12e .12 x15) = $13,912.

Est time: 01-05

11.

1.      FV = 10,000,000 x (1.06)4 = 12,624,770.

1.      FV = 10,000,000 x (1 + .06/12)(4 x 12) = 12,704,892.

1.      FV = 10,000,000 x e(4 x .06) = 12,712,492.

Est time: 01-05

12.