How much investment per dollar of expected annual operating savings can a company afford if the investment has an expected life of 8 years and its required rate of return is 14%?
To determine how much investment per dollar of expected annual operating savings a company can afford, we will use the concept of Net Present Value (NPV) and the required rate of return.
Step 1: Calculate the present value (PV) of expected annual operating savings.
- Identify the expected annual operating savings amount.
- Determine the required rate of return. In this case, it is given as 14%.
- Determine the number of years for which the savings are expected. In this case, it is 8 years.
- Use the formula for calculating the present value of an annuity to find the PV:
PV = (Annual Operating Savings) * [(1 - (1 + r) ^ -n) / r], where r is the required rate of return and n is the number of years.
Step 2: Calculate the maximum investment amount.
- The maximum investment amount is calculated by dividing the PV by the number of dollars invested.
- Let x be the maximum investment per dollar of savings.
- The maximum investment amount = PV / x
Now, let's plug in the values and calculate the answer.
Given:
- Expected life of the investment = 8 years
- Required rate of return = 14%
Using the formula for calculating the present value of an annuity:
PV = (Annual Operating Savings) * [(1 - (1 + r) ^ -n) / r]
Assuming the annual operating savings are $1, the calculation becomes:
PV = $1 * [(1 - (1 + 0.14) ^ -8) / 0.14]
PV ≈ 4.5429
Now, let's calculate the maximum investment amount:
Maximum Investment Amount = PV / x
Let x be the maximum investment per dollar of savings.
To find x, rearrange the equation:
x = PV / Maximum Investment Amount
Substituting the values:
x = 4.5429 / 1 ≈ $4.54
Therefore, the company can afford approximately $4.54 of investment per dollar of expected annual operating savings.