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 how much you need to invest today so that it grows to a given future amount at a specified rate of return. 

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. 

Which of the following investments that pay will $5,000 in 12 years will have a higher price today? 

The security that earns an interest rate of 8.25%. 

The security that earns an interest rate of 5.50%. 

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 13.80%. 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 eleven years 

An investment that matures in ten years 

Which of the following is true about present value calculations? 

Other things remaining equal, the present value of a future cash flow decreases if the investment time period increases. 

Other things remaining equal, the present value of a future cash flow increases if the investment time period increases.

Answer 1

Answer 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.

Answer b.

Security with interest rate of 8.25%:

Present value = Future amount / (1 + Interest rate)^Period
Present value = $5,000 / 1.0825^12
Present value = $1,931.24

Security with interest rate of 5.50%:

Present value = Future amount / (1 + Interest rate)^Period
Present value = $5,000 / 1.0550^12
Present value = $2,629.91

The security that earns an interest rate of 5.50% will have a higher price today.

Answer c.

Investment with maturity of 11 years:

Present value = Future amount / (1 + Interest rate)^Period
Present value = $1,000 / 1.1380^11
Present value = $241.23

Investment with maturity of 10 years:

Present value = Future amount / (1 + Interest rate)^Period
Present value = $1,000 / 1.1380^10
Present value = $274.52

An investment that matures in eleven years will exhibits lower price.

Answer d.

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