Question

Darin Clay, the CFO of Make Money.com, has to decide between the following two projects: 

Year	Project Million	Project Billion
0	-$1,700	-$I_(0)
1	I_(0)+210	I_(0)+650
2	1,010	1,450
3	1,450	2,100

The expected rate of return for either of the two projects is 14 percent. What is the range of initial investment (l0) for which Project Billion is more financially attractive than Project Million? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) 

Answer 1

Let cash flows in Year n be denoted by CFn

Project with higher NPV will be more attractive

NPV = ΣCFn/(1+r)ⁿ

Rate of return = r = 14%

For Project Million, NPV = -CF0 + CF1/(1+r) + CF2/(1+r)² + CF3/(1+r)³
= -1700 + (I₀+210)/(1+0.14) + 1010/(1+0.14)² + 1450/(1+0.14)³
= 0.877I₀ + 240.081

For Project Billion, NPV = -CF0 + CF1/(1+r) + CF2/(1+r)² + CF3/(1+r)³
= -I0 + (I₀+650)/(1+0.14) + 1450/(1+0.14)² + 2100/(1+0.14)³
= -0.122I₀ + 3103.344

For Project to be more attractive, NPV of Billion > NPV of Million

=> -0.122I₀ + 3103.344 > 0.877I₀ + 240.081

=> I₀ < (3103.344 - 240.081)/(0.877 + 0.122)

=> I₀ < $2866.13