Question

You own a 10-acre vineyard and earn income by selling your grapes to wineries. Your vineyard is currently planted to Merlot grapes, but you are thinking of replanting with Syrah grapes because they are commanding a higher market price per ton. Merlot fetches $1700 per ton but Syrah sells for $2700 per ton, those prices are expected to remain stable, and you produce 50 tons per year. Either way, you plan to sell the vineyard 5 years from today (at the end of the year) for 5-times (5x) the annual income (in year 5) from the sale of grapes (that is, you'll get the income from grape sales and then sell the vineyard for 5 times that amount at the end of year 5). However, if you were to switch to Syrah, switching will cost you $100,000 today and the vines won’t produce any grapes until the end of year 4 (that is, years 1 - 3 will have no sales if you plant Syrah, but years 4 and 5 will). The applicable discount rate is 11% per year. What is the NPV of switching? Round to the nearest cent. [Hint: Create a timeline showing the incremental annual cash flows from switching and find their NPV. Some cash flows will be negative (first 3 years) and some will be positive (years 4 and 5)]

Answer 1

Selling price of Merlot Grapes = $1,700 per ton
Selling price of Syrah Grapes = $2,700 per ton
Annual Sale = 50 tons

Alternative A : Selling Merlot Grapes
Annual Selling price for Year 1 to 5 = $1,700
Annual Sales = Annual Selling Price * No of Units
                        = $1,700 * 50
                        = $85,000

Sale price of Vineyard 5 years from today = 5 * Annual Income in year 5 from the sale of Merlot grapes.
                                                                                   = 5 *$ 85,000
                                                                                   = $425,000

Alternative B : Selling Syrah Grapes
Annual Selling price for Year 1 to 3 = 0 (No Sale)
Annual Selling price for Year 4 to 5 = $2,700
Annual Sales in Year 4 and 5 = Annual Selling Price * No of Units
                                                   = $2,700 * 50
                                                   = $135,000

Sale price of Vineyard 5 years from today = 5 * Annual Income in year 5 from the sale of Merlot grapes.
                                                                                   = 5 *$ 135,000
                                                                                   = $675,000

Calculation of Incremental annual cash flows from Switching :
Cost of switching = $100,000 today

Calculation of incremental yearly cash flows :
Incremental year cash flows = Annual Sales from Syrah Grapes – Annual Sales from Merlot Grapes.
Year 1 to 3 = 0 – $85,000 = $-85,000
Year 4 to 5 = $135,000 - $85,000 = $50,000

Incremental cash flow from sale of Vineyard = Sale value when growing Syrah Grapes – Sale value when growing Merlot Grapes
                                = $675,000 - $425,000
= $250,000

Incremental annual cash flows from Switching :
Year0 = $-100,000
Year1 = $-85,000
Year2 = $-85,000
Year3 = $-85,000
Year4 = $50,000
Year5 = $50,000 + $250,000 + $300,000

Discount rate = 11%

Calculation of NPV from Switching :
NPV of a project is the difference between the PV of cash inflows and PV of cash outflows. If NPV of a project is positive it should be accepted, otherwise it should be rejected.

NPV is given by = [CF1/(1+r)] + [CF2/(1+r)2] + [CF3/(1+r)3] +   …… [CFn/(1+r)n] + - CF0

Where

CF1 = Net Incremental Cash Inflow in Year 1

r = Discounting Rate or WACC

CF0 = Net Incremental Initial Cash Outflow

NPV = -100000 + (-85000/1.11) + (-85000/1.112) + (-85000/1.113) + (50000/1.114) + (-300000/1.115)
NPV = -100000 + (-76576.58) + (-68987.91) + (-62151.27) + (32936.55) + (178035.40)
NPV = $-96,743.81

Since NPV of switching is negative we should not switch from Merlot to Syrah.