Question

You have been offered a 5-year investment at a price of $50,000. It will pay $6,000 at the end of Year 1, $9,000 at the end of Year 2, and a fixed but currently unspecified cash flow, X, at the end of Years 3 through 5. The payer is essentially riskless, so you are sure the payments will be made, and you regard 3% as an appropriate rate of return on riskless 5-year investments. What cash flow must the investment provide at the end of each of the final 3 years, that is, what is X?

a. $12,996.53

b. $13,386.43

c. $13,724.80

d. $14,136.55

e. $15,261.73

Answer 1

The value of X can be calculated with the help of net present value concept using appropriate rate of return,

$50,000=\frac{6,000}{1.03}+\frac{9,000}{1.03^{2}}+X\times \left ( \frac{1-1.03^{-3}}{0.03} \right )\times \frac{1}{1.03^{2}}$

$50,000=5,825.24+8,483.36+X\times2.8286\times 0.9426$

$35,691.40=X\times2.66$

$13,386.43=X$

The correct option is b.