Question

What is the NPV of a project that costs $10,000 today and another $10,000 in one year, and is then expected to generate 8 annual cash inflows of $4,000 each starting at the end of year 6? The expected return on the market is 9.4%, the risk-free rate is 2% and the project’s beta is 1.4

Answer 1

The cash flows are:
Year 0: -$10,000
Year 1: -$10,000
Year 2: $0
Year 3: $0
Year 4: $0
Year 5: $0
Year 6: $4,000
Year 7: $4,000
Year 8: $4,000
Year 9: $4,000
Year 10:$4,000
Year 11:$4,000
Year 12:$4,000
Year 13:$4,000

To calculate the net present value we need to first calculate the discount rate which is calculated as:
=Risk free rate + Beta*(Expected return on the market - Risk free rate)
=2% + 1.4*(9.4% - 2%)
=2% + 1.4*0.074
=2% + 0.1036
=0.1236

Net present value=-Initial cash out flows + present value of future cash flows using the discount rates
=-10000/(1+0.1236)^0 - 10000/(1+0.1236)^1 + 0/(1+0.1236)^2 + 0/(1+0.1236)^3 + 0/(1+0.1236)^4 + 0/(1+0.1236)^5 + 4000/(1+0.1236)^6 + 4000/(1+0.1236)^7 + 4000/(1+0.1236)^8 + 4000/(1+0.1236)^9 + 4000/(1+0.1236)^10 + 4000/(1+0.1236)^11 + 4000/(1+0.1236)^12 + 4000/(1+0.1236)^13

=-10000/1 - 10000/1.1236 + 0/1.26247696 + 0/1.418519112 + 0/1.593848075 + 0/1.790847697 + 4000/2.012196472 + 4000/2.260903956+ 4000/2.540351685 + 4000/2.854339153 + 4000/3.207135472 + 4000/3.603537417 + 4000/4.048934641 + 4000/4.549382963

=-10000 - 8899.9644 + 0 + 0 + 0 + 0 + 1987.877454 + 1769.203857+ 1574.585135 + 1401.375164 + 1247.218908 + 1110.020388 + 987.9141934 + 879.2401151
=-7942.53

Answer: Hence, the NPV of the project is -$7942.53