Question

On 1/1/2004, an insurance company invested $1,000,000 developing an annuity product that will produce returns of $150,000 per year for the next 10 years (assume at the end of each year) following which the product will have to be abandoned.

The net present value of the project is $100,000.

At the end of 5 years, the opportunity cost of capital for the project decreased by 3 percentage points (or 3%), with the rest of the project remaining unchanged.

The insurance company recalculates the net present value as the present value of the remaining cash flows at the new opportunity cost of capital.

Find the value of the project on 1/1/2009.

a.

485,000

b.

535,000

c.

585,000

d.

635,000

e.

685,000

Answer 1

The correct alternative is "E" that is 685000.

We know,

NPV = Total inflow as on Today - Total Outflow as on Today.

Given, NPV = $100,000

Inflow = $ 150,000 every year for 10 years.

Outflow = $ 1,000,000 in current year.

let, opportunity cost be r%

Therefore, 100000 = {150000 * Present value of Annuity Factor ( 10years, r%) } - 1000000

Present value of annuity factor (10yrs, r%) = 7.3333

let, r be 5%, then Present value of annuity factor (10yrs, r%) = 7.7217

Again, let r be 6%, Present value of annuity factor (10yrs, r%) = 7.3601

Again, let r be 7%, Present value of annuity factor (10yrs, r%) = 7.0236

Thus, applying interpolation we get,

(r-7/6-7) =( 7.3333- 7.0236)/(7.3601-7.0236)

r = 6.0796

Now, after 5 years opportunity cost decreases by 3%

Thus, current discounting rate = 6.0796% - 3% = 3.0796%

Value of the project on 1/1/2009 = $150000 * Present value of annuity factor (5yrs, 3.0796%) = $685000.