The payback period is the number of years it takes to recover the initial cost of the investment.
Discounted payback method uses the present value of the estimated cash flows; it gives the number of years to recover the initial investment in present value terms.
Drawbacks of discounted payback method:
Compute the payback period and the discounted payback period assuming a rate of 10%.
|Cumulative Cash flows||-800||-460||-120||220||560|
|Discounted Cash flows||-800||309.1||280.99||255.45||232.22|
|Cumulative Discounted Cash flows||-800||-490.9||-209.91||45.54||277.76|
Payback period = Last year with negative cumulative cash flow + unrecovered cost at the beginning of the next year/ cash flow in the next year
Payback period = = 2.35 years
Discounted payback period = = 2.82 years
The discounted payback period is always going to be greater than the payback period, as long as the interest rate is positive. If the interest rate is 0%, both payback periods will be the same.
The average accounting rate of return (AAR) can be defined as:
Average accounting rate of return =
Profitability Index is the present value of a project’s future cash flows divided by the initial investment.
Profitability Index PI =
Profitability Index PI =
Investment decision rule for PI:
Invest if PI > 1.
Do not invest if PI < 1.
Difference between PI and NPV
Consider two projects A and B. Project A has an initial investment of $1 million and an NPV of 0.1 million. Project B has an initial investment of $1 billion and an NPV of 0.2 million. If projects A and B are mutually exclusive, then project B would be chosen because of higher NPV. But, if you consider the profitability index, it gives a different picture.
PI of project A = 1 + 0.1/1 = 1.1
PI of project B = 1 + 0.2 /1000 = 1.0002
Based on PI, project A is more profitable than project B.
NPV profile is a graph that plots a project’s NPV for different discount rates. The NPV is shown on the y-axis with the discount rates on the x-axis. Given the data below, create the NPV profile for project X.
|Discount rate||NPV (in $ million)|
Two important points on the graph:
Draw the NPV profiles for projects X and Y. Discuss the significance of crossover point.
The NPV profile for projects X and Y at different discount rates is tabulated below. Based on these values, the NPV profiles are depicted graphically.
Note: The values are computed for each discount rate using the calculator.
|Discount Rate (in %)||NPV for Project X||NPV for Project Y|
Let us plot the NPV profile for both the projects now.
The point at which the NPV for both projects intersect is called the crossover point.
If X and Y are mutually exclusive, the discount rate is used to decide which project is better. At lower discount rates, i.e., to the left of the crossover point, Project Y is better. At higher discount rates, i.e., to the right of the crossover point, Project X is better. For example, at a discount rate of 10%, Project Y is better, whereas at a discount rate of 20%, Project X is better.