Exercises: Investment appraisal: payback, NPV, and IRR

You are offered a choice between receiving $\$20\,000$ today or receiving $\$20\,000$ in one year's time. a) Explain which you would choose and why, using the concept of the time value of money (you can invest it today and have more in a year's time). b) Relate this concept to compounding (taking today's money into the future) and discounting (bringing future money to its present value).

An investment requires an initial outlay of $\$240\,000$ and generates different cash flows each year: $\$100\,000$ in the first, $\$80\,000$ in the second, and $\$80\,000$ in the third. a) Calculate its payback period by adding up the cash flows year by year until the outlay is recovered, and express it in years and months. b) Explain in your own words what the payback period measures and why companies with low liquidity favour it so much.

The figure represents an investment on a timeline: an initial outlay today and three annual cash inflows. We know that the investment recovers the outlay right at the end of Year 3. a) Calculate the Year 3 cash flow, marked with "?". b) State the payback period for this investment.

A project requires an initial outlay of $\$360\,000$ and will generate cash flows of $\$220\,000$ in one year and $\$242\,000$ in two years. The discount rate is $10\ \%$. a) Calculate the NPV: $VAN = -A + \frac{F_1}{(1 + k)} + \frac{F_2}{(1 + k)^2}$. b) Interpret the sign of the result and decide whether the project should be accepted, giving reasons for your answer.

An investment of $\$480\,000$ promises increasing cash flows: $\$220\,000$ in the first year, $\$242\,000$ in the second year, and $\$266\,200$ in the third year, with a discount rate of $10\ \%$. a) Calculate the NPV by discounting the three cash flows. b) Interpret the result: how much value does the project create after recovering the investment and providing a return on capital of $10\ \%$ per annum?

A project costs $\$200\,000$ today and will return a single payment of $\$230\,000$ in one year's time. a) Calculate its IRR, that is, the rate $r$ that makes the NPV equal to zero: set up $-200\,000 + \frac{230\,000}{1 + r} = 0$ and solve for $r$. b) If the company requires a minimum required rate of return of $12\ \%$, decide whether to accept the project by comparing the IRR with that rate. c) What if the required rate of return were $18\ \%$? State the IRR decision rule in your own words.

An investment requires $\$400\,000$ today and yields $\$220\,000$ after one year and $\$242\,000$ after two years. a) Verify numerically that with a discount rate of $10\ \%$ the NPV is exactly zero, making this rate the project's IRR. b) Explain in your own words what the IRR means: what annual yield the invested money returns to the project. c) If the company can obtain financing at $8\ \%$, reason whether it should accept the project; what if financing costs $12\ \%$?

A company is evaluating two projects with the same initial outlay of $\$220\,000$ and a discount rate of $10\ \%$: the SHORT project returns $\$220\,000$ in Year 1 and $\$48\,400$ in Year 2; the LONG project returns nothing until Year 3, when it yields $\$330\,000$ (it is a plantation that takes three years to produce its first harvest). a) Calculate the payback period for each project, in years and months. b) Calculate the NPV of each project, rounding to the nearest pesos. c) Verify that the two criteria rank the projects in opposite order, explain why this happens, and justify which criterion is more reliable for decision-making and why.

A Chief Financial Officer boasts: "I only use the payback period; if the money comes back quickly, the project is good, and the rest is redundant." Prove him wrong using this example: Project A costs $\$200\,000$ and yields $\$120\,000$, $\$120\,000$, and $\$0$ in the first three years; Project B costs the same and yields $\$80\,000$, $\$80\,000$, and $\$160\,000$. a) Calculate the payback period for both and check which one that CFO would choose. b) Compare the total cash flows generated by each project and highlight the two things that the payback period ignores: what happens after the initial outlay is recovered and the time value of money. c) Conclude why NPV is a more comprehensive criterion.