Question

Hodgkiss Enterprises has gathered projected cash flows for two projects.

Year	Project I		Project J
0	–$	259,000	–$	259,000
1		114,100		90,400
2		104,800		99,900
3		88,800		101,900
4		77,800		108,900

At what interest rate would the company be indifferent between the two projects? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
  

Interest rate             %

Which project is better if the required return is above this interest rate?
  

Answer 1

Let r be the interest rate for indifferent between two projects.

So NPV for Project I=NPV for Project J

PV=CF/(1+r)^n

CF=cash flow

n= year in which cash flow occur

NPV for Project I= sum of PV of cash flow - Initial Investment

NPV for Project I=114100/(1+r)^1+104800/(1+r)^2+88800/(1+r)^3+77800/(1+r)^4 - 259000

NPV for Project J= 90400/(1+r)^1+99900/(1+r)^2+101900/(1+r)^3+108900/(1+r)^4 - 259000

so

114100/(1+r)^1+104800/(1+r)^2+88800/(1+r)^3+77800/(1+r)^4 - 259000= 90400/(1+r)^1+99900/(1+r)^2+101900/(1+r)^3+108900/(1+r)^4 - 259000

-23700/(1+r)^1-4900/(1+r)^2+13100/(1+r)^3+31100/(1+r)^4 =0

So solving for r we get

r=18.81%

Let New interest rate is 20% which is greater than 18.81% .

NPV for Project I= 114100/(1+20%)^1+104800/(1+20%)^2+88800/(1+20%)^3+77800/(1+20%)^4 - 259000=$-2230.71 Eq 1

NPV for Project J= 90400/(1+20%)^1+99900/(1+20%)^2+101900/(1+20%)^3+108900/(1+20%)^4 - 259000=-$2804.39 Eq 2

From equation 1 and 2 we know that NPV for project I is greater than Project J. So project I is better than project J.