Question

Use this data to answer the following questions: Purchase Price: $155,000 Down Payment: $25,000 Balance to be carried at 8% for 15 years 3Year holding period Appreciation is expected to be 10% over the holding period Use 9% discount factors YEAR CASH FLOW 1 $1,400 2 $1,600 3 $1,700 Compute the Net Present Value (NPV) Compute the Internal Rate of Return

Answer 1

Loan Amount = $155000 - $25000 = $130000

Loan value after three years which is to be repaid = $130000* 1.08^3 = $163762.56

Value of property after three years = $155000 *1.1^3 = $206305

So Terminal cash flow at the end of year 3 = $206305 - $163762.56 = $42542.44

So

NPV = -25000+ 1400/1.09+1600/1.09^2+1700/1.09^3+42542.44/1.09^3

=$11794.37

IRR (r) is the rate of return at which NPV = 0 and is given by

-25000+ 1400/(1+r)+1600/(1+r)^2+1700/(1+r)^3+42542.44/(1+r)^3 = 0

Using hit and trial method

r= 0.20 gives the LHS = 2881.04

r= 0.30 gives the LHS = -2838.67

r= 0.25  gives the LHS = -203.87

r=0.24   gives the LHS = 374.21

So, r lies between 0.24 and 0.25. So using linear approximation method

r= 0.24+ (374.21-0)/(374.21-(-203.87))*(0.25-0.24) = 0.2464

which is correct

So IRR is 24.64%