Question

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 $6,000 in 7 years will have a higher price today? 

• The security that earns an interest rate of 7.00%. 

• The security that earns an interest rate of 10.50%. 

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 11.00%. 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 eight years 

• An investment that matures in seven 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 discount rate increases. 

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

Answer b.

If interest rate is 7.00%:

Present value = Future value / (1 + Interest rate)^Period
Present value = $6,000 / 1.07^7
Present value = $3,736.50

If interest rate is 10.50%:

Present value = Future value / (1 + Interest rate)^Period
Present value = $6,000 / 1.1050^7
Present value = $2,982.74

The security that earns an interest rate of 7.00% will have a higher price today.

Answer c.

Investment with maturity period of 8 years:

Present value = Future value / (1 + Interest rate)^Period
Present value = $1,000 / 1.11^8
Present value = $433.93

Investment with maturity period of 7 years:

Present value = Future value / (1 + Interest rate)^Period
Present value = $1,000 / 1.11^7
Present value = $481.66

An investment that matures in eight years will exhibit the lower price.

Answer d.

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