Answer to Question #224382 in Finance for Nayeem

Question

time value and discount rates You just won a lottery that promises to pay you $1,000,000 exactly 10 years from today. Because the $1,000,000 payment is guarnteed by the state in which you live, opportunities exist to sell the claim today for an immediate single cash payment. a. What is the least you will sell your claim for if you can earn the following rates of return on similar-risk investments during the 10-year period? (1) 6% (2) 9% (3) 12% b. Rework part a under the assumption that the $1,000,000 payment will be received in 15 rather than 10 years. c. On the basis of your findings in parts a and b, discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum.

Answer 1

a)

$PV=\frac{FV}{(1+i)^n}$

FV=future value

PV=present value

r=annual interest rate

n=number of periods interest held

$1.\frac{ 1000000}{(1.06)^{10}} = \$558394\\ 2. \frac{1000000}{(1.09)^{10}} = \$422411 \\ 3. \frac{1000000}{(1.12)^{10}} = \$321973$

b)

$1.\frac{ 1000000}{(1.06)^{15}} = \$ 417265\\ 2. \frac{1000000}{(1.09)^{15}} = \$ 274538 \\ 3. \frac{1000000}{(1.12)^{15}} = \$ 182696$

c)

As time period increases, the expected minimum present value decreases and as interest rate increases, the expected minimum present value decreases.