Question

Receiving much less media attention from the previous case, the newly chosen CFO of Retro Max (RM) was thrilled with the response received from drug companies for the latest discovery, a unique electronic stimulator that reduces the pain from arthritis. While the process had yet to pass Federal Drug Administration (FDA) testing and was in the mid-stages of development, excitement from the investment community extreme. RM received the three proposal described in the following paragraph. (Use a 10% interest rate throughout this analysis unless otherwise specified.)

Proposal 3: A trust fund would be set up for the next eight years. At the end of that period, RM CFO would receive the proceeds (and discount them back to the present at 10%). The trust fund called for semiannual payments for the next eight years of $200,000 (a total of $400,000 per year).

The payments would start immediately. Since the payments are coming at the beginning of each period instead of the end, this is an annuity due. Assume the annual interest rate on this annuity is 10% annually (5 percent semiannually). Determine the present value of the trust fund's final value.

Required: Find the present value of each of the three offers and indicate which one has the highest present value. (Show and label all calculations.)

Receiving much less media attention from the previous case, the newly chosen CFO of Retro Max (RM) was thrilled with the response received from drug companies for the latest discovery, a unique electronic stimulator that reduces the pain from arthritis. While the process had yet to pass Federal Drug Administration (FDA) testing and was in the mid-stages of development, excitement from the investment community extreme. RM received the three proposal described in the following paragraph. (Use a 10% interest rate throughout this analysis unless otherwise specified.)

Proposal I: $1,000,000 now plus $200,000 from year 6 through 15. Also if the product did over $100 million in cumulative sales by the end of year 15, RM would receive an additional $3,000,000. RM CFO thought there was a 70% probability this would happen.

Proposal 2: Thirty percent of the buyer's gross profit on the product for the next four years. The buyer in this case was Amce Pharmaceutical. Amce’s gross profit margin was 60%. Sales in year one were projected to be $2 million and then expected to grow by 40% per year.

Proposal 3: A trust fund would be set up for the next eight years. At the end of that period, RM CFO would receive the proceeds (and discount them back to the present at 10%). The trust fund called for semiannual payments for the next eight years of $200,000 (a total of $400,000 per year).

The payments would start immediately. Since the payments are coming at the beginning of each period instead of the end, this is an annuity due. Assume the annual interest rate on this annuity is 10% annually (5 percent semiannually). Determine the present value of the trust fund's final value.

Required: Find the present value of each of the three offers and indicate which one has the highest present value. (Show and label all calculations.)

Answer 1

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SOLUTION

(A) proposal 1

$1,000,000 now + $200,000 from year 6 through 15 (Deferred Annuity)

Appendix D (PV Factor)

PV_A = A × PV_IFA(10%, 10 years) = $200,000 × 6.145 = $1,229,000 (Present Value at the beginning of year 6, i.e. the end of year 5)

Appendix B (PV Factor)

PV = FV × PV_IF(10%, 5 years) = $1,229,000 × 0.621 = $763,209

Appendix B (PV Factor)

.70 × $3,000,000 = $2,100,000
PV = FV × PV_IF(10%, 15 years) = $2,100,000 × 0.239 = $501,900

Total Value

$1,000,000 (Present Payment)
+$763,209 (Present Value Of Deferred Annuity)
+$501,900 (Present Value Of $3 million Bonus)
_________
$2,265,109
_________

(B) proposal 2

Year Sales   Gross Profit (60% Of Sales) Payment (30% Of Gross Profit)
1 $2,000,000 $1,200,000 $360,000
2 $2,800,000 $1,680,000 $504,000
3 $3,920,000 $2,352,000 $705,600
4 $5,488,000 $3,292,800 $987,600

Year Payment Appendix B (PV Factor) PV

1 $360,000 0.909 $327,240
2 $504,000 0.826 $416,304
3 $705,600 0.751 $529,906
4 $987,600 0.683 $674,531
__________
Total Value $1,947,981
__________

(C) proposal 3

Future Value Of An Annuity Due (Appendix C)

On Semiannually Basis
n = 16 + 1 = 17
i = 10%/2 = 5%
FV_IFA = 25.840 – 1 = 24.840 (Appendix C)

FV_A = A × FV_IFA = $200,000 × 24.840 = $4,968,000 (Value After 8 Years)
Present Value Of Trust Fund (Appendix B)
PV = A × PV_IF(10%, 8 years) = $4,968,000 × 0.467 = $2,320,056 (Total Value)

SUMMARY

Value of Offer 1 $2,265,109
Value of Offer 2 $1,947,981
Value of Offer 3 $2,320,056