Question

PIUulen J (1J PLS). The Bachelor and the Bachelorette have hired you to determine who has the best endorsement offer. The Bachelor has been offered the job as a spokesperson for the National I Like Myself Foundation as they figure that they do not have to offer any advice for him to do the job. The NILMF will pay him $2,000 per month starting ten years from today for a total of 120 months. He then will receive $40,000 per year for six years with the first payment of $40,000 occurring one month after the last payment of $2,000. He also will receive $70,000 every year for five years with the first of these coming six months from today. The Bachelorette has been offered a job as the spokesperson for the Do You Believe I Get Paid For What I Do Foundation. The DYBIGPFWIDF will pay her $30,000 per year for twenty years with the first of these coming today. She will also receive $400,000 six months after her last payment of $30,000. Finally she will receive $500,000 fifty years from today - she was worried that she would not have enough for a 75th birthday gift for herself. They want to know who has the best offer in today's dollars. Assume a 9% (compounded monthly) rate for your analysis. Show all of your work and give a total value for each of their offers.

Answer 1

Solution

P.S => All working notes are in the end

Interest Rate => 9% Per Annum (Compounded Monthly)

Effective Monthly Interest Rate => 0.75% (9%/12)

Effective Semi Annually Interest Rate =>

{[(1.0075)^6 - 1] X 100} = 5.585%

Effective Annual Interest Rate =>

{[(1.0075)^12 - 1] X 100} = 9.381%

1) Bachelor's Offer

A) Data in Question

$2,000 per month for 120 months starting 10 years from today

$40,000 per year for 6 years (1st Payment after 1 month of of last Payment of $2,000. That is one month after 20 years from today)

$70,000 per year for 5 years (Starting 6 months from Today)

B) Calculation of Present Value of his Offer

Payment 1 ($2,000)

($2,000 X 79.534) X0.4079 = $64, 883.84

(Refer Working Note 1 for detailed explanation of the above)

Payment 2 ($40,000)

$32,052.29

(Refer Working Note 2 for detailed explanation of the above)

Payment 3 ($70,000)

(Refer Working Note 3 for detailed explanation of the above)

$279,296

Total = Payment 1 + Payment 2 + Payment 3 = $376,232.13

Bachelorette Offer

A) Data in Question

Payment 1 = $30,000 per year for 20 years starting today

Payment 2 = $400,000 (6 months after last Payment of above)

Payment 3 = $500,000 after 50 years from today

B) Calculation of present value

Payment 1 = $30,000 X 9.7196 = $291,588

Payment 2 = $63,039.26 (Refer Working Note 4)

Payment 3 = $500,000 X 0.1130 = $56,500

Total = $411,127.26

As prove from above Offer of Bachelorette is better in today's dollar terms

Working Notes

1)

79.534= Cumulative Present Value Factor of monthly receipts for 10 years.

($2,000 X 79.534) Gives Present value of 120 monthly receipts as on date of 1st Receipt , which is 10 years from today (Calculated using monthly effective rate of 0.75%)

0.4079 = Present Value Factor of 10 years. It discounts the above amount, as result of Which we get present value as on today (Calculated using effective annual rate of 9.381%)

2)

Last $2,000 Payment will be 20 Years and one month from today)

(i) Present Value of all the receipts as on date of first Receipt

$40,000 X 4.8515 = $194,060

(ii) Present Value of above as on beginning of that month (that is 20 years from now)

$194,060 X 0.9926 = $192,624

(iii) Present Value as on today of the above

$192,624 X 0.1664 = $32,052.29

3)

(i) Present Value of receipts as on 6 months from Today

$70,000 X 4.2128 = $294,896

(ii) Present Value of above as on today

$294,896 X 0.9471 (Calculated using 6 month effective rate) = $279,296

4)

(i) Present Value of $400,000 after 20 Years (AS Receipt will be 20 Years 6 Month from today)

= $400,000 X 0.9471 = $378, 841.70

(ii) Present Value of above today

= $378, 841.70 X 0.1664 = $63,039.26