Question

Proposal 1

Pay the family of Boone $300,000 a year for the next 20 years, and $500,000 a year for the remaining 20 years.

Proposal 2

Pay the family a lump sum payment of $5 million today.

Proposal 3

Pay the family of Boone a relatively small amount of $50,000 a year for the next 40 years, but also guarantee them a final payment of $75 million at the end of 40 years.

In order to analyze the present value of these three proposals, attorney Knox Hollister called on a financial expert to do the analysis. You will aid in the process.

Required

1. Assume a discount rate of 6 percent is used, which of the three projects has the highest present value?

In analyzing the first proposal, take the present value of the

20-year $300,000 annuity. Then take the present value of

the deferred annuity of $500,000 that will run from the 21st through the 40th year. The answer you get for the second annuity will represent the value at the beginning of the 21st year (the same as the end of the 20th year). You will need to discount this lump sum value back for 20 years as a single amount to get its present value. You then add together the present value of the first and second annuity.

The second and third proposals are straightforward and require no further explanation.

2. Now assume that a discount rate of 11 percent is used instead of

6 percent. Which of the three alternatives provides the highest present value?

3. Explain why the change in outcome takes place between question 1 and question 2.

4. If Knox Hollister thinks additional punitive damages are likely to be $4 million in a jury trial, should he be more likely to settle out-of-court or go before the jury?

Answer 1

Ans 1) Proposal 3rd provide the highest present value which is $ 8,043,978.92

Discount Rate = 6%

See the calculation of each proposal.

Net Present Value = Cash Flow * (1- ((1+r)^-n) / r)

Proposal 1 =

To Calculate PV we will split this in 2 parts –

• 1^st we will calculate PV of 300,000 for initial 20 years
• 2^nd we will calculate PV of 500,000 for 40 years and then deduct PV of 500,000 for initial 20 years. This will give us PV of 500,000 from 21^st year to 40^th year

300,000 for initial 20 years = ((300,000*(1- ((1+0.06)^-20)) /0.06) = 3,440,976.37

500,000 for remaining 20 years = {((1-((1+0.06)^-40))/0.06)*500000} – {((1-((1+0.06)^-20))/0.06)*500000} = 1,788,187.82

Total from Proposal 1 = 3,440,976.37 + 1,788,187.82 = 5,229,164.19

Proposal 2 = Straight Away 5,000,000 today so PV is same.

Proposal 3 =

• PV of 50,000 a year for 40 years
• PV of onetime payment of 75,000,000 at the end of 40 years

50,000 for 40 years = ((50,000*(1- ((1+0.06)^-40)) /0.06) = 752,314.84

75 million at the end of 40^th year = 75,000,000/1.06^40 = 7,291,664.08

Total from Proposal 3 = 752,314.84 + 7,291,664.08 = 8,043,978.92

Ans 2) At discount rate 11% proposal 2 offer the highest NPV.

If discount rate is 11%

Proposal 1 =

300,000 for initial 20 years = 300,000 * ((1-((1+0.11)^-40))/0.11) = 2,685,315.25

500,000 for remaining 20 years = {((1-((1+0.11)^-40))/0.11)*500000} – {((1-((1+0.11)^-20))/0.11)*500000} = 493,861.35

Total from Proposal 1 = 2,685,315.25 + 493,861.35 = 3,179,176.60

Proposal 2 = Straight Away 5,000,000 today so PV is same.

Proposal 3 =

50,000 for 40 years = ((50,000*(1- ((1+0.11)^-40)) /0.11) = 447,552.54

75 million at the end of 40^th year = 75,000,000/1.06^40 = 1,153,830.76

Total from Proposal 3 = 447,552.54 + 1,153,830.76 = 1,601,383.30

Ans 3) Reason of changes in question 1 and question 2 is discount rate. In Question 1 we are discounting future flows at 6% only and in question 2 we are discounting the future flow at 11%, it means in project 2 our expectation is high, we look for more returns so if we need more returns we look for more inflows. In this case though we are discounting at higher rate but returns are same so denominator value increases and numerator is same so the output will be less.

Ans 4) He should g for out of court settlement as if he goes for jury trial there will be additional outflows of 4 million which would further reduce NPV so better opt for out of court settlement.

Hope this helps. Feel free to share your feedback. Thanks and have a good day.