For an investment ending at time T we denote the net cash flow at time t by c_t and the net rate of cashflow per unit time by (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 : Give the yield equation for this problem. Determine whether the yield of this investment is (approximately) 1.1%, 1.3%, 1.5%, 1.7% or 1.9%.

They are multiple-choice question

Answer: We obtain, in millions of

a)NPV(i)=-22.475-10v+_0^47(1+i)^(-t)dt at rate i

b)NPV(i)=22.475+10v-_0^47(1+i)^(-t)dt at rate i

c)NPV(i)=-22.475-10v+_3^50(1+i)^(-t)dt at rate i

d)NPV(i)=22.475+10v-_3^50(1+i)^(-t)dt at rate i

The net cash flow changes sign a).only once b). more than once, so the yield i₀ a).exist b).does not exist .

The approximate yield is a). 1.1% b). 1.3% c). 1.7% d). 1.9% , found by plugging the candidate values into the yield equation a).NPV(i)=0 b). NPV(i)=T c). A(i)=0 d). A(i)=T