In: Finance
Consider a project generating the following cash flows over six years:
Year Cash Flow (R in millions)
0 -59.00
1 4.00
2 5.00
3 6.00
4 7.33
5 8.00
6 8.25
Required:
1. Calculate the NPV over six years. The discount rate is 11%.
2. This project does not end after the sixth year but instead will generate cash flows far into the future. Estimate the terminal value, assume that cash flows after year 6 will continue at R8.25 million per year in perpetuity, and then recalculate the investment's NPV.
3. Calculate the terminal value, assume that cash flows after the sixth year grow at 2% annually in perpetuity, and then recalculate the investment's NPV.
Solution :- | ||||||||||
(a) | ||||||||||
Year | Cashflows | PVF@11% | PV of Cashflows | |||||||
0 | -59 | 1 | -59 | |||||||
1 | 4 | 0.901 | 3.604 | |||||||
2 | 5 | 0.812 | 4.058 | |||||||
3 | 6 | 0.731 | 4.387 | |||||||
4 | 7.33 | 0.659 | 4.828 | |||||||
5 | 8 | 0.593 | 4.748 | |||||||
6 | 8.25 | 0.535 | 4.411 | |||||||
NPV | = | -32.96 | ||||||||
(b) | Terminal Value at year 6 of R8.25 upto perpetuity | = | 8.25/11% | = | 75.00 | |||||
Year | Cashflows | PVF@11% | PV of Cashflows | |||||||
0 | -59 | 1 | -59 | |||||||
1 | 4 | 0.901 | 3.604 | |||||||
2 | 5 | 0.812 | 4.058 | |||||||
3 | 6 | 0.731 | 4.387 | |||||||
4 | 7.33 | 0.659 | 4.828 | |||||||
5 | 8 | 0.593 | 4.748 | |||||||
6 | 8.25 | 0.535 | 4.411 | |||||||
T6 | 75 | 0.535 | 40.098 | |||||||
NPV | = | 7.134 | ||||||||
© | Terminal Value at year 6 of R8.25 with growth 2% annually | = | 8.25(1+0.02)/(0.11-0.02) | = | 93.5 | |||||||
Year | Cashflows | PVF@11% | PV of Cashflows | |||||||||
0 | -59 | 1.000 | -59.000 | |||||||||
1 | 4 | 0.901 | 3.604 | |||||||||
2 | 5 | 0.812 | 4.058 | |||||||||
3 | 6 | 0.731 | 4.387 | |||||||||
4 | 7.33 | 0.659 | 4.828 | |||||||||
5 | 8 | 0.593 | 4.748 | |||||||||
6 | 8.25 | 0.535 | 4.411 | |||||||||
T6 | 93.5 | 0.535 | 49.989 | |||||||||
NPV | = | 17.025 | ||||||||||