For an investment ending at time T we denote the net cash flow at time t by
Question:
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 : 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%.
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