Question

1) Your firm is presented with an opportunity to purchase a ski lodge today for $2.4 million. In one year, the lodge will generate cash of $200,000 if it was a good snow season and $120,000 if it was a bad snow season. These amounts will both grow by 2% each year (so in year 2, if snow is good, you receive $204,000; bad, $122,400). Each year, the chance of good snow is 75%. Your firm would run this lodge forever. The required rate of return is 12%. What is the NPV of purchasing the ski lodge?

2) A candy business currently generates $200,000 in cash flow each year, in perpetuity. Assume each year's entire cash flow arrives at the end of the year. It is considering adding a second assembly line. Doing so will increase total annual cash flow to $350,000 each year. The expansion project will cost $1.25 million, paid today, and be finished in time to fully impact this year's cash flow.

The required return is 12%. What is the NPV of this expansion project (in thousands)?

Answer 1

Answer (1)

PV of cash flows in case of good snow season = Annual cash flow in Year 1 / (required rate of return - growth rate)

= 200000 /(12% - 2%)

= $2,000,000

PV of cash flows in case of bad snow season =120000 /(12% - 2%)

= $1,200,000

Hence:

NPV = Expected PV of cash flows - Initial Investment = (2000000 * 75% + 1200000 * 25%) - 2400000 = -$600,000

NPV = - $600,000 or   ($600,000)

Answer (2):

Incremental annual cash flows in perpetuity = 350000 - 200000 = $150,000

NPV = PV of perpetual cash flows - Initial investments

= 150000 / 12% - 1250000

= $0

NPV = $0