“Evaluating Investment Risk: Calculating Worst-Case NPV for a Costly Venture at 10% Required Return”

QUESTION

An investment under consideration has a payback of eight years and a cost of $877,000. Assume the cash flows are conventional.

If the required return is 10%, what is the worst-case NPV? (Negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round the final answer to 2 decimal places. Omit $ sign in your response.)

Worst-case NPV           $

ANSWER

“Evaluating Investment Risk: Calculating Worst-Case NPV for a Costly Venture at 10% Required Return”

The worst-case Net Present Value (NPV) of an investment is a critical metric in financial analysis, as it helps assess the potential risk and return associated with a particular project. In this scenario, we are evaluating an investment with a payback period of eight years and a cost of $877,000, assuming conventional cash flows. The required return for this investment is 10%. We are tasked with calculating the worst-case NPV.

NPV is a financial metric used to determine the profitability of an investment by comparing the present value of its expected cash flows to its initial cost. In the worst-case scenario, we need to consider the possibility that the investment may not perform as well as expected, leading to lower cash flows or even losses.

The formula for calculating NPV is:

���=∑���(1+�)�−�0NPV=∑(1+r)tCFt​​−C0​

Where:

���CFt​ represents the cash flow at time $t$,

$r$ is the required rate of return (10% in this case),

$t$ is the time period, and

�0C0​ is the initial cost of the investment.

In this specific scenario, the initial cost (�0C0​) is $877,000, and we will need to calculate the cash flows for each year and discount them back to the present value using the required return rate of 10%. The payback period of eight years indicates that we will consider cash flows for eight years.

Now, let’s calculate the worst-case NPV by considering the possibility that the investment generates the lowest possible cash flows each year:

Year 1: -$100,000 (Initial investment) Year 2: -$100,000 Year 3: -$100,000 Year 4: -$100,000 Year 5: -$100,000 Year 6: -$100,000 Year 7: -$100,000 Year 8: -$100,000

In this worst-case scenario, the investment doesn’t generate any positive cash flows; it only incurs costs. Now, we can calculate the worst-case NPV:

���=−100,000(1+0.10)1+−100,000(1+0.10)2+−100,000(1+0.10)3+−100,000(1+0.10)4+−100,000(1+0.10)5+−100,000(1+0.10)6+−100,000(1+0.10)7+−100,000(1+0.10)8−877,000NPV=(1+0.10)1−100,000​+(1+0.10)2−100,000​+(1+0.10)3−100,000​+(1+0.10)4−100,000​+(1+0.10)5−100,000​+(1+0.10)6−100,000​+(1+0.10)7−100,000​+(1+0.10)8−100,000​−877,000

Calculating this expression:

���=−100,0001.10+−100,0001.102+−100,0001.103+−100,0001.104+−100,0001.105+−100,0001.106+−100,0001.107+−100,0001.108−877,000NPV=1.10−100,000​+1.102−100,000​+1.103−100,000​+1.104−100,000​+1.105−100,000​+1.106−100,000​+1.107−100,000​+1.108−100,000​−877,000

Now, compute the NPV:

$NPV=-90,909.09-82,644.63-75,131.48-68,301.35-62,092.14-56,445.59-51,309.63-46,639.66-877,000$

$NPV=-1,319,463.86$

So, the worst-case NPV for this investment, assuming a required return of 10%, is approximately -$1,319,463.86. The negative sign indicates that, in the worst-case scenario, the investment is expected to result in a significant loss. It’s crucial for investors to consider such worst-case scenarios to make informed decisions and assess the associated risks.