You own a thriving restaurant but want to change careers. Your brother offers to buy the business with the following monthly payments: $2,750 at the end of each month for 4 years, followed by $3,000 at the end of each month for 3 years. Assuming that you can earn 9% compounded monthly, what is the equivalent cash price of your brother’s offer? (NPV)
To find the equivalent cash price of your brother's offer, we need to calculate the net present value (NPV) of the cash flows.
To do this, we will discount each cash flow using the present value formula, which is:
PV = FV / (1+r)^n
Where PV is the present value, FV is the future value (the cash flow), r is the interest rate per period, and n is the number of periods.
In this case, we have two sets of cash flows: $2,750 per month for 48 months, followed by $3,000 per month for 36 months. Let's calculate the net present value.
First, let's calculate the present value of the $2,750 payments. The interest rate per period is 9%/12 (since it is compounded monthly) and there are 48 payments.
PV1 = $2,750 / (1+(9%/12))^48
PV1 = $2,750 / (1+0.0075)^48
PV1 = $2,750 / (1.0075)^48
PV1 = $2,750 / 1.4743796
Next, let's calculate the present value of the $3,000 payments. Again, the interest rate per period is 9%/12 and there are 36 payments.
PV2 = $3,000 / (1+(9%/12))^36
PV2 = $3,000 / (1+0.0075)^36
PV2 = $3,000 / (1.0075)^36
PV2 = $3,000 / 1.3659585
Now, let's sum the present values of both sets of cash flows to get the net present value.
NPV = PV1 + PV2
Finally, the equivalent cash price of your brother's offer is the NPV.