Question

Finding a present value is the reverse of finding a future value.

Which of the following is true about finding the present value of cash flows?

Finding the present value of cash flows tells you what a cash flow will be worth in future years at a specified rate of return.

Finding the present value of cash flows tells you how much you need to invest today so that it grows to a given future amount at a specified rate of return.

Which of the following investments that pay will $18,000 in 4 years will have a lower price today?

The security that earns an interest rate of 6.00%.

The security that earns an interest rate of 4.00%.

Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 4.00%. Assuming that both investments have equal risk and Eric’s investment time horizon is flexible, which of the following investment options will exhibit the lower price?

An investment that matures in four years

An investment that matures in five years

Which of the following is true about present value calculations?

Other things remaining equal, the present value of a future cash flow increases if the discount rate increases.

Other things remaining equal, the present value of a future cash flow decreases if the discount rate increases.

Answer 1

Ans:- (a) Finding the present value of cash flows tells you how much you need to invest today so that it grows to a given future amount at a specified rate of return. option (b) is the right answer.

(b) In this part, we need to find which investment has a lower price today If it pays $18,000 in 4 years.

Present Value is given by Future Value / (1+r)^n where r is the rate of return

If r=6%, then PV=$18,000 / (1+0.06)^4 = $14,257.69.

If r=4%, then PV=$18,000 / (1+0.04)^4 = $15,386.48.

Therefore, the security that earns an interest rate of 6.00% will have a lower price today. option (a) is the right answer.

(c) FV is given $1,000 and r is 4%.

If n=4, then PV = $1,000 / (1+0.04)^4 = $854.80

If n =5, then PV = $1,000 / (1+0.04)^5 = $821.93

Therefore, the investment that matures in five years will exhibit a lower price today. option (b) is the right answer.

(d) After analysis from part (b) it is clear that if other things remaining equal, the present value of a future cash flow decreases if the discount rate increases. option (b) is the right answer.

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