Question

Medical Research Corporation (Comprehensive time value of money) 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 electronic stimulator that reduces the pain from arthritis. The process had yet to pass rigorous 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 following this paragraph. (A 10 percent interest rate should be used throughout this analysis unless otherwise specified.)

Offer 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, he would receive an additional $3,000,000. Dr. Wolf thought there was a 70 percent probability this would happen.

Offer II - 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.

Offer III - A trust fund would be set up for the next eight 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 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. 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.

Answer 1

Offer 1:
To find out the present value, all the future cash flows are to be discounted. $1,000,000 is not required to be discounted as it is received now. Additional $3,000,000 to be received at the end of 15 years has a probability of 70%. So we will take only 70% of its present value.
PV = 1,000,000 + 200,0000/(1+10%)^6 + 200,0000/(1+10%)^7 + 200,0000/(1+10%)^8…………….200,0000/(1+10%)^15 + 70% of 3000,000(1+10%)^15
PV = $ 2,265,782
Calculation as below:
	(A)	(B)	(C) = (A)/(B)
	Amount	PV Factor	PV
Year 0	10,00,000	0	10,00,000
Year 6	2,00,000	(1+10%)^6	1,12,895
Year 7	2,00,000	(1+10%)^7	1,02,632
Year 8	2,00,000	(1+10%)^8	93,301
Year 9	2,00,000	(1+10%)^9	84,820
Year 10	2,00,000	(1+10%)^10	77,109
Year 11	2,00,000	(1+10%)^11	70,099
Year 12	2,00,000	(1+10%)^12	63,726
Year 13	2,00,000	(1+10%)^13	57,933
Year 14	2,00,000	(1+10%)^14	52,666
Year 15	2,00,000	(1+10%)^15	47,878
Year 15*	21,00,000	(1+10%)^15	5,02,723
Total			22,65,782
*70% of $3,000,000 = $ 210,000 as there is 70% probability of receiving additional $3,000,000

Offer 2:
First, we will calculate the sales for the next four years.
Sales
Year 1	20,00,000
Year 2	2,000,000 + 40% of 2,000,000 = 2,800,000
Year 3	2,800,000 + 40% of 2,800,000 = 3,920,000
Year 4	3,920,000 + 40% of 3,920,000 = 5,488,000

Now, we will discount the 30% of the gross margin on the yearly sales for next four years.
	A	B = A * 60%	C = B * 30%	D	E = C/D
	Sales	Gross Margin (60% of sales)	30% of Gross Margin	PV Factor	PV
Year 1	20,00,000	12,00,000	3,60,000	(1+10%)^1	3,27,273
Year 2	28,00,000	16,80,000	5,04,000	(1+10%)^2	4,16,529
Year 3	39,20,000	23,52,000	7,05,600	(1+10%)^3	5,30,128
Year 4	54,88,000	32,92,800	9,87,840	(1+10%)^4	6,74,708
Total					19,48,637

PV = $ 1,948,637

Offer 3:
We can calculate the future value of the trust fund by adding all the future values of all the semi annual cash flows or directly by multiplying the semi annual cash flow with the annuity due future value factor from the table.
Method 1. Future value of all semi annual cash flows
	A	B	C = A*B
	Amount	FV Factor	Future value at end of 8 years
Beginning of first half of year 1	200000	(1+10%)^8	4,28,718
Beginning of 2nd half of year 1	200000	(1+10%)^7.5	4,08,766
Beginning of first half of year 2	200000	(1+10%)^7	3,89,743
Beginning of 2nd half of year 2	200000	(1+10%)^6.5	3,71,606
Beginning of first half of year 3	200000	(1+10%)^6	3,54,312
Beginning of 2nd half of year 3	200000	(1+10%)^5.5	3,37,823
Beginning of first half of year 4	200000	(1+10%)^5	3,22,102
Beginning of 2nd half of year 4	200000	(1+10%)^4.5	3,07,112
Beginning of first half of year 5	200000	(1+10%)^4	2,92,820
Beginning of 2nd half of year 5	200000	(1+10%)^3.5	2,79,193
Beginning of first half of year 6	200000	(1+10%)^3	2,66,200
Beginning of 2nd half of year 6	200000	(1+10%)^2.5	2,53,812
Beginning of first half of year 7	200000	(1+10%)^2	2,42,000
Beginning of 2nd half of year 7	200000	(1+10%)^1.5	2,30,738
Beginning of first half of year 8	200000	(1+10%)^1	2,20,000
Beginning of 2nd half of year 8	200000	(1+10%)^0.5	2,09,762
Total Future value			49,14,708
Future value of the trust fund = 4,914,708
Now Present value of this trust fund value = FV discounted by 10% for 8 years
PV = 4,914,708 * (1+10%)^8
PV= 2,292,747

Method 2:Multiplying the semi annual cash flow with the annuity due future value factor from the table.
FV factor for 10 cash flows ( 5 years * 2 as there are two paymenmts every year) for 5% interest rate (10% annual interest rate divided by 2 for semiannual interest rate) is 24.8404 from the table
Future value = 200,000*24.8404
Future value of the trust fund = 4,968,080
Now Present value of this trust fund value = FV discounted by 10% for 8 years
PV = 4,968,080 * (1+10%)^8
PV= 2,317,646
Please note that method 1 gives the exact values while method 2 gives an approximate value

After comparing all the offers, Offer 3 has highest present value