1. Is the following statement true or false? The PV of a future payment is large

Question

1. Is the following statement true or false? The PV of a future payment is larger the greater the number of periods and the higher the discount (interest) rate. Provide a TVM example to illustrate the logic behind the correct response.

2. What is the present value of a 3-year ordinary annuity of $100 plus an additional $200 at the end of Year 3 if the annual interest rate is 10%? Show a time line of the cash flows, then show "calculator key strokes" that produce the correct PV.

3. Assume that you plan to buy a boat 5 years from now. You have no funds now, but you think you can save $5,000 per year. You plan to invest the funds in securities that you think will provide a 10% after-tax annual rate of return. If you make the first of the 5 deposits immediately, how much will you have available to spend on the boat at the end of the 5th year? Show a time line of the cash flows, then show "calculator key strokes" that produce the correct PV.

Explanation / Answer

1.

The Present value of a future payment is larger the greater the number of payments – False

As the length of time until payment grows, present value declines. Present value tends to become small as the time horizon grows. If you look out far enough, they will always get close to zero. Example: ABC Co. offers you a saving certificate of $100 to be paid in 25 years to try their new product. So what is the PV of $100 paid 25 years later with discount rate @10%?

1/1.1025 = 1/10.8347 = 0.0923

So, 0.0923*$100 = $9.23 will be paid after 25 years.

Well, it’s enough to draw the customers, but it’s not $100.

The Present value of a future payment is larger the higher the discount (interest) rates – False

Present value and Discount rates are inversely related. Thus, higher the discount rate, lower the present value.

Say in previous example, let take the discount rate as 15%.

1/1.1525 = 1/32.9189 = 0.0303

So, 0.0303*$100 = $3.03 will be paid after 25 years.

2. PV = 300*PVAF(10%,3yrs) + 200*PVIF(10%,3yr)

PV = 300*2.4869 + 200*0.7514

PV = 398.97

398.97

3.  

Year Cash Flow PVAF(10%,n) PV 1 100 2 100 3 100 2.4869 248.69 3 200 0.7514 150.28

398.97

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