Questions 1, 2 and 3 1. Find the correct sentence (a) PV of $100 received in Yea

Question

Questions 1, 2 and 3

1. Find the correct sentence (a) PV of $100 received in Year 10 at a discount rate of 1% is $91.53 (b) PV of $100 received in Year 10 at a discount rate of 13% is $28.46 (c) PV of $100 received in Year 15 at a discount rate of 25% is $3.618 (d) PV of $100 received in each years 1 through 3 at a discount rate of 12% is $240.18 2. If the two-year discount factor is 0.8264, what is the two-year discount rate? (a) 0.01 (b)0.1 (c) 0.2 (d) 0.3 3. As winner of a competition, you can choose one of the following prizes. If the interest rate is 12%, which is the most valuable prize? (a) $100,000 now. (b) $180,000 at the end of five years c) $11,400 a year forever (d) $19,000 for each of 10 years

Explanation / Answer

(1) (a)

PV = $100 x P/F(1%, 10) = $100 x 0.9053 = $90.53

(2) (b)

2-year discount rate = (1 + r)-2 = 0.8264

(1 + r)2 = 1/0.8264 = 1.2100

Taking square roots on each side,

1 + r = 1.10

r = 0.10 = 10%

(3) (d)

PV of option (a) = $100,000

PV of option (b) = $180,000 x P/F(12%,5) = $180,000 x 0.5674** = $102,132

PV of option (c) = $11,400 / 0.012 = $95,000

PV of option (d) = $19,000 x P/A(12%, 10) = $19,000 x 5.6502** = $107,354

Since option (d) has highest PV, this is most valuable.

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