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: Suppose that the infrastructure fund now wants to adjust the above cash flows to account for a constant rate of inflation e of 1% per annum. The fund can borrow at an interest rate of 1.5% per annum. Calculate the net present value at this interest rate, allowing for inflation. Is the yield ie0 allowing for inflation larger or smaller than 1.5%?
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: Suppose that the infrastructure fund now wants to adjust the above cash flows to account for a constant rate of inflation e of 1% per annum. The fund can borrow at an interest rate of 1.5% per annum. Calculate the
Answer: The formula for the net present value with inflation is, with i = 1.5% and measured in millions of £, a). NPV(i)= -22.475-10(1+e)/(1+i)+∫_0^47[(1+e)/(1+i)]^t dt b). NPV(i)= 22.475+10(1+e)/(1+i)-∫_0^47[(1+e)/(1+i)]^t dt c). NPV(i)= -22.475-10(1+e)/(1+i)+∫_3^50[(1+e)/(1+i)]^t dt d). NPV(i)= 22.475+10(1+e)/(1+i)-∫_3^50[(1+e)/(1+i)]^t dt at rate i.
Hence the NPVe(i) = a). -£8.9017m b). £8.9017m c). -£9.51852m d). £9.51852 . The yield will be a).lower b). higher than 1.5%, as the sign changes once from a).negative to positive b). positive to negative
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