Question

8) The British government has consol bonds (perpetuities) outstanding that pay £100 per year forever. Assume that the current discount rate is 4% a) What is the value of the bond today in £? b) If this consol trades in the market today at £2,480, what rate of return will an investor earn from this investment? 9) The Elysian Trust has set up a program that provides free school education for underprivileged children in India and Nepal. The Elysian Trust will provide, as endowment, $1 million each year-end in perpetuity. The interest rate is 8% per year What is the value of this gift today? Suppose, instead, Elysian provides an endowment that pays $2 million every two years in perpetuity, what is the value of this gift today? Suppose, instead, Elysian provides an endowment that pays S500,000 every six months in perpetuity, what is the value of this gift today? a) b) c)

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Answer 1

(8) (a) Perpetual Periodic Payments of the Bond = £ 100, Discount Rate = 4 %

As the cash flows from the bond constitute a perpetuity, the value of the bond today should be equal to the present value of this perpetuity so as to conform with the principles of time value of money and law of one price.

Bond Value = 100 / 0.04 = £ 2500

(b) Actual Bond Value = £ 2480 and Periodic Perpetual Cash Flows = £ 100

Let the rate of return be R

Therefore, 2480 = 100 / R

R = (100 / 2480) = 0.040323 or 4.03 %

NOTE: Please raise separate queries for solutions to the remaining unrelated questions as one query is restricted to the solution of only one complete question (with a maximum of four sub-parts)