Question

Part A: Explain how Net Present Value (NPV) is used in evaluating capital budgeting proposals. Part B: Imagine that you are given a $12,000 entrance scholarship to study at Brock University. Fortunately, over the years your parents have managed to save for your education through the purchase of an RESP. Therefore, you are able to invest the $12,000 for the next four years at an interest rate of 5%. How much money will you have after four years of investing the $12,000? In other words, what is the future value of $12, 000 invested over four years at a 5% interest rate? Be sure to show your calculations. In your response, be sure to incorporate properly the terms: Time Value of Money and Compounding. Lastly, using the Rule of 72, how many years will it take to double the initial investment? Part C: Now that the IOC has made the decision to postpone the Tokyo Summer 2020 Olympics until next year, one of the sponsoring organizations finds itself with Olympic merchandise that needs to be liquidated. When you heard about this opportunity you became quite excited because you are an avid collector of Olympic merchandise. In fact, when you graduate from Brock University, you plan on opening an Olympic memorabilia shop. The offer from this Olympic sponsor is such that you have the option to purchase the merchandise entirely upfront for $10,500 or to pay $2,750 per year for the next four years (with payments at the beginning of the year). Assuming a discount rate of 7%, is it advisable to pay the cost of the merchandise entirely upfront? Explain. Be sure to show your calculations.

Answer 1

Part A:

NPV is used to evaluate if capital budgeting proposals generate value for the firm's investors.

The NPV is calculated as the sum of present values of cash inflows, minus the initial investment.

If the sum of present values of cash inflows is higher than the initial investment, the proposal generates value for the firm's investors and should be accepted. If the sum is lower, the proposal does not generate value for the firm's investors and should be rejected.

Part B:

future value = present value * (1 + interest rate)number of years

future value = $12,000 * (1 + 5%)4

future value = $14,586.08

Part C:

It is advisable to pay upfront only if the upfront cost is lower than the sum of present values of annual payments.

Present value of each annual payment = annual payment / (1 + discount rate)n

where n = number of years after which the annual payment occurs.

Each payment occurs at the beginning of the year, hence the first payment occurs at year 0, the second at year 1, and so on.

Sum of present values of annual payments = ($2,750 / (1 + 7%)0) + ($2,750 / (1 + 7%)1) + ($2,750 / (1 + 7%)2) + ($2,750 / (1 + 7%)3)

Sum of present values of annual payments = $9,966.87

This is lower than the upfront cost.

Therefore, it is not advisable to pay the cost of the merchandise entirely upfront because the present value of annual payments is lower than the upfront cost.