Question

Your first job out of college will pay you $84,000 in year 1 (exactly one year from today). You estimate that your salary will grow at 6% per year for 45 years (compounded annually), when you'll stop working. If the applicable discount rate is 12%, what is the present value of these future earnings today? Round to the nearest cent.

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 $1,200 per ton but Syrah sells for $3,000 per ton, those prices are expected to remain stable, and you produce 5 tons per acre (so 50 tons per year total). Either way, you plan to sell the vineyard 5 years from now (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 switch to Syrah, it will cost you $150,000 immediately and the vines won’t produce any grapes until 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 15% per year. From a pure economic standpoint, should you switch to Syrah?

Answer 1

Present Value of growing annuity = P/(r-g)[1-{(1+g)/(1+r)}ⁿ]

= 84,000/(0.12-0.06)[1-{(1+0.06)/(1+0.12)}⁴⁵]

= 1,400,000*0.9161

= $1,282,488.34

Present Value of income from Merlot = 1,200*50*PVAF(15%, 5 years) + 1,200*50*5*PVF(15%, 5 years)

= 60,000*3.352 + 300,000*0.497

= $350,220

From Syrah, NPV = 3,000*50*PVF(15%, 4 years) + 3,000*50*PVF(15%, 5 years) + 3,000*50*5*PVF(15%, 5 years) – 100,000

= 150,000*0.572 + 150,000*0.497 + 750,000*0.497 – 100,000

= $433,100

Since present value of income of Syrah is higher, You should switch to Syrah