Question

Tesla is planning production of its new car the Model X. It will require an initial cost of $500 million. The initial price of Model X will be $80,000 and the cost per unit will be $40,000. Tesla’s cost of capital is 20 percent. Assume that the initial investment expenditure is required at t = 0 but sales begin in year t = 1.

(a) Suppose that Tesla expects to sell 10,000 Model X cars per year for five years then the production will stop. If the price and cost of production remain constant over the five years, what is the NPV of the Model X at t = 0?

(b) Now suppose that Tesla expects to sell 10,000 Model X cars per year for ten years after which production will cease. If the price and cost of production remain constant over the ten years, what is the NPV of the model X at t = 0?

(c) Now suppose that Tesla expects to sell 10,000 Model X cars per year for ever. If the price and cost of production increase by 5 percent per year for ever, what is the NPV of the Model X at t = 0?

(d) Again suppose that Tesla expects to sell 10,000 Model X cars per year for ever. If now the price of the Model X increases by 5 percent forever, but the cost of production increases by 7.5 percent forever, what is the NPV of the Model X at t = 0?

Answer 1

NPV= C0+ CF1/(1+r)^1 + CF2/(1+r)^2 …………CFn/(1+r)^n

= CF0 + PV of annuity

=CF0 + Annuity*(1-1/(1+rate)^number of terms)/rate

A:Here annuity = Net profit

=Profit per unit* number of units

= (80000-40000)*10000

= 400000000

NPV = -500,000,000+   400,000,000 *(1-1/1.2^5)/0.2

=696,244,856

B: Here

NPV = -500,000,000+ 400,000,000 *(1-1/1.2^10)/0.2

= 1,176,988,834.22

C: Here PV of annuity = Annuity/r

NPV = -500,000,000+ 400,000,000/0.2

= 1,500,000,000.00

D: Here annuity = Net profit

=Profit per unit* number of units

= (80000*105%-40000*107.5%)*10000

= 410,000,000.00

NPV = -500,000,000+ 410,000,000/0.2

= 1,550,000,000