Question

Please show all the steps you've done to reach the final answer. I am trying to learn, so please show your work. Typing your answer is important.

A) How much must you deposit each year into your retirement account starting now and continuing through year 8 if you want to be able to withdraw $80,000 per year forever, beginning 29 years from now? Assume the account earns interest at 13% per year.

B). If a manufacturer of electronic devices invests $650,000 in equipment for making compact piezoelectric accelerometers for general purpose vibration measurement, estimate the rate of return from revenue of $225,000 per year for 10 years and $70,000 in salvage value from the used equipment sale in year 10.

C) . During recessionary periods, bonds that were issued many years ago have a higher coupon rate than currently issued bonds. Therefore, they may sell at a premium, a price higher than their face value, because of currently low coupon rates. A $50,000 bond that was issued 15 years ago is for sale for $58,000. What rate of return per year will a purchaser make if the bond coupon rate is 20% per year payable semi-annually, and the bond is due 5 years from now?

Answer 1

Ans 1)

We are going to invest amount "X" from year 1 to year 8

FW of this Payment at year 8 would be X*(F/A,13%,8)=14.415X

Now through year 9 to year 29 we are neither investing any new deposit nor withdrawing hence with return of 13% we have deposit worth 14.415X(1.13)^20=166.11X at the year 29

Now we are going to withdraw $80000 per year henceforth

166.11X=80000+80000/(1.13)+80000/(1.13)^2+...+infinite times

166.11X=80000(1/(1-(1/1.13)))=80000*(1.13)/0.13=695384.62

X=695384.62/166.11=4186.29

Hence we have to deposit amount equals to $4186.29 each year through Year 1 to Year 8

Ans 2)

Rate of Return is that interest rate which makes NPW=0

PW of Revenues=PW of Costs

225000(P/A,i%,10)+70000(P/F,i%,10)=650000

225000(P/A,i%,9)+295000(P/F,i%,10)=650000

Using Excel solver we get Rate of Return equals to 32.79%

Ans 3)

Current Price of Bond= Sum of Present Worth of Future Coupon payments + PW of Face Value

58000=50000*0.1(P/A/i%,10)+50000*(P/F,i%,5)
58000=5000(P/A,i%,10)+50000(P/F,i%,10)

i%=7.6527%..Semiannual return

Hence rate of return per year is 15.3054% when the bond is due 5 years from now