Question

# Sharon is making an investment of \$80,000 today and expects to receive \$2,000 each year for...

Sharon is making an investment of \$80,000 today and expects to receive \$2,000 each year for the next five years. At the end of the fifth year, a sum of \$100,000 will be returned. What is the internal rate of return compounded annually on this investment?

a) 6.84% b) 6.86% c) 6.88% d) 7.02%

 6% 7% Period Cash Flow Discountig Factor [1/(1.06^period)] PV of cash flows (cash flow*discounting factor) Discountig Factor [1/(1.07^period)] PV of cash flows (cash flow*discounting factor) 0 -80000 1 -80000 1 -80000 1 2000 0.9433962 1886.79245 0.9345794 1869.158879 2 2000 0.8899964 1779.99288 0.8734387 1746.877457 3 2000 0.8396193 1679.23857 0.8162979 1632.595754 4 2000 0.7920937 1584.18733 0.7628952 1525.790424 5 102000 0.7472582 76220.3336 0.7129862 72724.59031 NPV = 3150.54486 NPV = -500.98718

IRR is the rate of return at which NPV=0

Here, NPV@6% is positive and @7% is negative.

Therefore, IRR is between 6% and 7%

IRR = Rate at which positive NPV + [Positive NPV/(Positive NPV-Negative NPV)]

= 6% + [3150.54/(3150.54-(-500.99)]

= 6% + [3150.54/3651.53]

= 6% + 0.86% = 6.86%