Question

Intro

You've estimated the following cash flows (in $ million) for two mutually exclusive projects:

Year	Project A	Project B
0	-28	-43
1	30	45
2	40	50

  Attempt 1/5 for 10 pts.

Part 1

What is the crossover rate, i.e., the discount rate at which both projects have the same NPV?

The crossover rate is the discount rate at which both projects have the same NPV:

NPV(A) = NPV(B)
⇔ NPV(A) - NPV(B) = 0
⇔ NPV(A-B) = 0

	A	B	C	D
1	Year	Project A	Project B	Difference A-B
2	0	-28	-43	15
3	1	30	45	-15
4	2	40	50	-10

NPV of cash flow differences:

NPVA−B =(CF0,A−CF0,B)+CF1,A−CF1,B1+r+CF2,A−CF2,B(1+r)2=0NPVA-B =(CF0,A-CF0,B)+CF1,A-CF1,B1+r+CF2,A-CF2,B(1+r)2=0

⇔ 15+−151+r+−10(1+r)2=015+-151+r+-10(1+r)2=0

We can use the quadratic formula, trial and error, a financial calculator or Excel's IRR function to solve for r. Using Excel:
=IRR(D2:D4)

We then find that the crossover rate is 45.74%, or 0.457.Correct ✓

Part 2

What is project A's NPV at the crossover rate?

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

B C D E Year Project A -$28,000,000.00 $30,000,000.00 $40,000,000.00 Project B $43,000,000.00 $45,000,000.00 $50,000,000.00 Differential CF $15,000,000.00 $15,000,000.00 $10,000,000.00 2 Cross over rate 45.74% NPV of A at cross over rate $11,415,780.15 NPV of B at cross over rate $11,415,780.15

Cell reference -

ДА DE Year 4 O Project A -28000000 30000000 40000000 Project B Differential CF -43000000 =D4-C4 45000000 =D5-C5 50000000 =D6-C6 Cross over rate =IRR(E4:E6) NPV of A at cross over rate =C4+NPV(C8,C5:C6) NPV of B at cross over rate =D4+NPV(C8,D5:D6) 13 15.

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.