For an investment ending at time T we denote the net cash flow at time t by ct and the net rate of cashflow per unit time by ρ(t). The present time is t = 0 and time is measured in years. An infrastructure fund considers the construction of a new bridge. It estimates that the project will require an initial outlay of £22.475m = £22,475,000 and a further outlay of £10m after one year (m = million). There will be an estimated inflow of toll charges of £1m per annum payable continuously for 47 years, beginning at time t = 3. Task : Assume that the fund may borrow or lend money at 1.0% per annum. Determine whether or not the business venture is profitable, and find the profit or loss when the project ends in 50 years’ time. Answer: It is clear that NPV(i) changes sign from a). positive to negative b).negative to positive at i0, as the outlays take place a). before b).after income is generated. Hence, a). 1%=i1i0 and the project is a). profitable b).not profitable . In fact, the profit in 50 years’ time is a)NPV(i_1)·(1+i_1)^50=£6.6774m b).NPV(i_1)·(1+i_0)^50=£8.5473m c).NPV(i_0)·(1+i_1)^50=£542.555 d).NPV(i_0)·(1+i_0)^50=£694.508 They are multiple-choice questions
For an investment ending at time T we denote the net cash flow at time t by ct and the net rate of cashflow per unit time by ρ(t). The present time is t = 0 and time is measured in years.
An infrastructure fund considers the construction of a new bridge. It estimates that the project will require an initial outlay of £22.475m = £22,475,000 and a further outlay of £10m after one year (m = million). There will be an estimated inflow of toll charges of £1m per annum payable continuously for 47 years, beginning at time t = 3.
Task : Assume that the fund may borrow or lend money at 1.0% per annum. Determine whether or not the business venture is profitable, and find the profit or loss when the project ends in 50 years’ time.
Answer: It is clear that NPV(i) changes sign from a). positive to negative b).negative to positive at i0, as the outlays take place a). before b).after income is generated.
Hence, a). 1%=i1<i0 b). 1%=i1=i0 c). 1%=i1>i0 and the project is a). profitable b).not profitable .
In fact, the profit in 50 years’ time is
a)NPV(i_1)·(1+i_1)^50=£6.6774m
b).NPV(i_1)·(1+i_0)^50=£8.5473m
c).NPV(i_0)·(1+i_1)^50=£542.555
d).NPV(i_0)·(1+i_0)^50=£694.508
They are multiple-choice questions
Step by step
Solved in 2 steps
