Question

Helga is considering the purchase of a small restaurant. The purchase price listed by the seller is $950,000. Helga has used past financial information to estimate that the net cash flows (cash inflows less cash outflows) generated by the restaurant would be as follows: years amount 1-6 $95,000 $785,000 $875,000 $965,000 $1,055,000. If purchased, the restaurant would be held for 10 years and then sold for an estimated $850,000. Required: Determine the present value, assuming that Helga desires a 9% rate of return on this investment. (Assume that all cash flows occur at the end of the year.)

Answer 1

To determine the present value, calculate the present value of each net cash flow and the future selling price of the restaurant using a rate of return of 9%. Add up all the present values to get the final value of $3,790,588.93.

Step-by-step explanation:

To determine the present value, we need to calculate the present value of each annual net cash flow and the future selling price of the restaurant. We will use the formula for calculating present value:

PV = CF / (1 + r)^n

CF = Cash flow, r = rate of return, n = number of years. Assuming a rate of return of 9%, the present values of the net cash flows would be:

Year 1: $95,000 / (1 + 0.09)^1 = $87,156.00

Year 2: $785,000 / (1 + 0.09)^2 = $663,284.98

Year 3: $875,000 / (1 + 0.09)^3 = $678,296.95

Year 4: $965,000 / (1 + 0.09)^4 = $690,880.92

Year 5: $1,055,000 / (1 + 0.09)^5 = $700,687.20

Year 6: $850,000 / (1 + 0.09)^6 = $564,726.57

To calculate the present value of the selling price, we use the formula:

PV = Selling price / (1 + r)^n

Year 10: $850,000 / (1 + 0.09)^10 = $405,556.31

Finally, we add up all the present values:

$87,156.00 + $663,284.98 + $678,296.95 + $690,880.92 + $700,687.20 + $564,726.57 + $405,556.31 = $3,790,588.93

Therefore, the present value of this investment is $3,790,588.93.