Question 174525: Can someone please help with this problem:
A company has two investment opportunities. Both investments cost $5,000 and will provide the following net cash flows:
Investment A: Year 1 = $3,000; Year 2 = $3,000; Year 3 = $3,000 ; Year 4 = $3,000
Investment B: Year 1 = $3,000; Year 2 = $4,000; Year 3 = $2,000; Year 4 = $1,000
The total present value of Investment A's cash inflow assuming a 10% minimum rate of return is (round to the nearest whole dollr):
a. $10,638
b. $9,510
c. $3,452
d. $3,000
Answer by actuary(112)   (Show Source):
You can put this solution on YOUR website! The problem can be solved by going back to basic principles. Each cash flow is discounted back to the date of the computation by multiplying the cash flow by (1/(1+rate of return))^(number of years from the date of the computation to the date of payment.
So the discounted cash flows are:
3000*(1/1.1)^1
3000*(1/1.1)^2
3000*(1/1.1)^3
3000*(1/1.1)^4
The four discounted cash flows are added together
3000*(1/1.1)^2 + 3000*(1/1.1)^2 + 3000*(1/1.1)^3 + 3000*(1.1)^4
= 3000
The sum of the 4 numbers in the brackets is called an annuity immediate. There is a formula for annuity immediates and can be easily calculated. This approach works because the cash flow each year is level. Otherwise, the basic principle's approach always works.
Larry
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