Question

An investment promises to pay $1,000 for the next three years, an unknown amount in the fourth year and $1,600 in the fifth year. What should the value of the fourth year payment be if the investment is required to yield 10% and is selling for $8,000? Please post work. Thank you

Answer 1

HI,

Here the cash flows are

Y1 Y2 Y3 Y4 Y5

$1,000 $1,000 $1,000 ? $1,600

lest say 4th year payment is x

yield r =10%

selling price P = $8,000

We know that selling price will be equal to present value of all cash flows discounted at yield rate

so P = Y1/(1+r)^1 +Y2/(1+r)^2 +Y3/(1+r)^3 +Y4/(!+r)^4 +Y5/(1+r)^5

8000= 1000/(1+10%) + 1000/(1+10%)^2 +1000/(1+10%)^3 +x/(1+10%)^4 +1600/(1+10%)^5

8000 = 1000/1.1 +1000/1.1^2 +1000/1.1^3 +x/1.1^4 +1600/1.1^5

x/1.1^4 = 4519.67

x= $6,617.26

Hence 4th year payment should be $6,617.26

Thanks