Question

Your fund has two groups of investors. The first invests in year zero, and the second invests in year three. Throughout the life of the fund, you pay the investors cash flows at the end of every year, as described below, ending in the final payout of all the remaining capital at the end of year five. Every cash flow is distributed to the investors proportional to their capital contribution; for example, if a group of investors contributed 50% of the capital in the fund, they will receive 50% of that year’s cash flows.

0 | 1 | 2 | 3 | 4 | 5 | |

capital contributions | 200,000 | 1,000,000 | ||||

cash flows | 200,000 | 200,000 | 100,000 | 100,000 | 1,500,00 |

Using a discount rate of 12%, please build a financial model to answer the following questions:

1. What is the periodic return for the entire 5-year holding period if all cash flows are reinvested at the discount rate?

2. What is the periodic return for the entire 5-year holding period if the cash flows are not reinvested—and instead are simply added to the final balance?

3. What is the internal rate of return (IRR) for the first group of investors?

4. What is the internal rate of return (IRR) for the second group of investors?

5. What is the net present value (NPV) for the first group of investors?

6. What is the net present value (NPV) for the second group of investors?

7. Why do you think the two investors earned different rates of return? What changed over time?

Answer #1

Part 1)

Reinvestment table:

Year |
Cashflow |
FVF @
12% |
Maturity value
(Cashflow* FVF @ 12%) |

1 | 200,000 | 1.12^4 = 1.57352 | 314,704 |

2 | 200,000 | 1.12^3 = 1.40493 | 280,986 |

3 | 100,000 | 1.12^2 = 1.25440 | 125,440 |

4 | 100,000 | 1.12000 | 112,000 |

5 | 1,500,000 | 1.00000 | 1,500,000 |

2,333,130 |

Part 3,4,5&6)

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