If you are willing to pay $41,601.00 today to receive $4,415.00 per year forever then your required rate of return must be ____%. Assume the first payment is received one year from today.

Answer 1

To find the required rate of return, we can use the formula for the present value of a perpetuity, which is given by:

\[ PV = \frac{C}{r} \]

where:

• \( PV \) = Present Value (the amount you are willing to pay today)
• \( C \) = Cash flow per period (the annual payment)
• \( r \) = rate of return (as a decimal)

In this case, the present value \( PV = 41,601 \) and the cash flow \( C = 4,415 \).

Rearranging the formula to solve for \( r \):

\[ r = \frac{C}{PV} \]

Now substituting the known values:

\[ r = \frac{4,415}{41,601} \]

Calculating \( r \):

\[ r \approx 0.1067 \]

To express it as a percentage:

\[ r \approx 0.1067 \times 100 \approx 10.67% \]

Therefore, your required rate of return must be approximately 10.67%.