Dr. Harold Wolf of Medical Research Corporation (MRC) was thrilled with the resp
ID: 2674572 • Letter: D
Question
Dr. Harold Wolf of Medical Research Corporation (MRC) was thrilled with the response he had received from drug companies for his latest discovery, a unique elec- tronic stimulator that reduces the pain from arthritis. The process had yet to pass rig- orous Federal Drug Administration (FDA) testing and was still in the early stages of development, but the interest was intense. He received the three offers described below this paragraph. (A 10 percent interest rate should be used throughout this analysis unless otherwise specified.)Offer I
Offer II
Offer III
$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, he would receive an additional $3,000,000. Dr. Wolf thought there was a 70 percent probability this would happen.
Thirty percent of the buyer’s gross profit on the product for the next four years. The buyer in this case was Zbay Pharmaceutical. Zbay’s gross profit margin was 60 percent. Sales in year one were projected to be $2 million and then expected to grow by 40 percent per year.
A trust fund would be set up for the next 8 years. At the end of that period, Dr. Wolf would receive the proceeds (and discount them back to the present at 10 percent). The trust fund called for semiannual payments for the next 8 years of $200,000 (a total of $400,000 per year).
The payments would start immediately. Since the payments are coming at the begin- ning of each period instead of the end, this is an annuity due. To look up the future value of an annuity due in the tables, add 1 to n (16 ?? 1) and subtract 1 from the value in the table. Assume the annual interest rate on this annuity is 10 percent 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.
Explanation / Answer
Offer I
$1,000,000 ------- plus
+ $200,000 from year 6 through 15
PVa= A x PV ifa (10% ,10 years)= =200000 x6.145=1,229,000
Appendix B
PVa= A x PVifa (10% ,5 years)
=1229 000 x .621= 763 209
+ .70 × $3,000,000 = $2,100,000
=======
Appendix B
PVa= A x PVifa (10% ,15 years)
=2,100 000 x .239= 501 900
=================
Total value of Offer I
$1,000,000 Payment today
763,209 Present value of deferred annuity
501,900 Present value of $3 million bonus
$2,265,109
=================================
Offer II
Gross Profit Payment 30%
Year Sales (60% of Sales) 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
Appendix B
Year Payment PV Factor PV
1 $360,000 .909 $327,240
2 504,000 .826 416,304
3 705,600 .751 529,906
4 987,600 .683 674,531
Total value of Offer II $1,947,981
=============================
Offer III
Future value of an annuity due (Appendix C)
8 years – semiannually
n = 16 + 1 = 17
i = 10%/2 = 5%
FVIFA = 25.840 – 1 = 24.840 (Appendix C)
FVa= A x FVifa
=200 000 x24 .840= 4968 000 value after 8 years
PV = A x PVif(10% , 8 years)
= 4 968 000 x .467
= 2,320 056--------value of offer iii
=======================================
Value of Offer I $2,265,109
Value of Offer II $1,947,981
Value of Offer III $2,320,056
Select -----------Offer III
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