Question

Linda Jones is deciding between two investment projects.

Choice 1

Linda can invest into a young biotech firm. She expects that she will need to pay this firm $35,000 at the end of each year for the next two years. After that, she expects to receive back from the firm $90,000 at the end of each year for 18 years.

Choice 2

Linda can invest $200,000 today into an AI firm. She expects to be paid $42,000 at the end of the year, and expects cash flows from the AI firm to increase by 5% every year, paid at the end of each year in perpetuity

1. “Draw” timelines (tables), showing cash flows of each investment.
2. Suppose Linda’s discount rate is 12%. Which project should she choose?
3. At which discount rate would Linda be indifferent between her two choices?

Answer 1

	Choice 2 Cash Flow in Year 1	$42,000
	Choice 2 Cash Flow in Year 2	$44,100	(42000*1.05)
	Choice 2 Cash Flow in Year (N+1)=1.05* Cash Flow in Year (N)
	TIMELINE   TABLE	N	Cash Flow
		Year	Choice 1	Choice2
		0	$0	-$200,000
		1	-$35,000	$42,000
		2	-$35,000	$44,100
		3	$90,000	$46,305
		4	$90,000	$48,620
		5	$90,000	$51,051
		6	$90,000	$53,604
		7	$90,000	$56,284
		8	$90,000	$59,098
		9	$90,000	$62,053
		10	$90,000	$65,156
		11	$90,000	$68,414
		12	$90,000	$71,834
		13	$90,000	$75,426
		14	$90,000	$79,197
		15	$90,000	$83,157
		16	$90,000	$87,315
		17	$90,000	$91,681
		18	$90,000	$96,265
		19	$90,000	$101,078
		20	$90,000	$106,132
		21	----------------------	$111,439
		22		$117,010
		23		$122,861
		24		$129,004
		25		$135,454
		26		$142,227
				In Perpetuity
	CALCULATION OF NET PRESENT VALUE
	CHOICE 1
	Present Value(PV) of Cash Flow:
	(Cash Flow)/((1+i)^N)
	i=discount rate =12%=0.12
	N=Year   of Cash Flow	N	CF	PV=CF/(1.12^N)
			Cash Flow	Present Value
		Year	Choice 1	of Cash Flow
		0	$0	$0
		1	-$35,000	-$31,250
		2	-$35,000	-$27,902
		3	$90,000	$64,060
		4	$90,000	$57,197
		5	$90,000	$51,068
		6	$90,000	$45,597
		7	$90,000	$40,711
		8	$90,000	$36,349
		9	$90,000	$32,455
		10	$90,000	$28,978
		11	$90,000	$25,873
		12	$90,000	$23,101
		13	$90,000	$20,626
		14	$90,000	$18,416
		15	$90,000	$16,443
		16	$90,000	$14,681
		17	$90,000	$13,108
		18	$90,000	$11,704
		19	$90,000	$10,450
		20	$90,000	$9,330
			SUM	$460,994
	Net Present Value =Sum of PV	$460,994
	CALCULATION OF NET PRESENT VALUE
	CHOICE 2
I	Initial Investment at year 0	-$200,000
	Present Value of perpetuity =CF1/(d-g)
	CF1=Cash inflow in year 1	$42,000
	d=discount rate=12%	0.12
	g=Growth Rate of Cash Floew=5%=	0.05
PV	Present Value of perpetuity =	$600,000	(42000/(0.12-0.05)
NPV=PV+I	Net Present Value	$400,000
	WE SHOULD CHOOSE CHOICE 1
	Choice 1 has higher Net Present Value
c	Indifferent Discount Rate
	This can be Calculated by Trial and Error with different discount rate =i
i	Choice 1
Discount Rate	Year	Cash Flow	Present Value
0.11	1	-$35,000	-$31,532
0.11	2	-$35,000	-$28,407
0.11	3	$90,000	$65,807
0.11	4	$90,000	$59,286
0.11	5	$90,000	$53,411
0.11	6	$90,000	$48,118
0.11	7	$90,000	$43,349
0.11	8	$90,000	$39,053
0.11	9	$90,000	$35,183
0.11	10	$90,000	$31,697
0.11	11	$90,000	$28,555
0.11	12	$90,000	$25,726
0.11	13	$90,000	$23,176
0.11	14	$90,000	$20,880
0.11	15	$90,000	$18,810
0.11	16	$90,000	$16,946
0.11	17	$90,000	$15,267
0.11	18	$90,000	$13,754
0.11	19	$90,000	$12,391
0.11	20	$90,000	$11,163
		NPV	$502,634
	CHOICE 2
	Net Present Value =-200000+(42000/(i-0.05))	$500,000
c	At Discount Rate of 11%, Linda will be indifferent between her two choices