Bond pricing: In class, we have discussed the pricing of bonds with finite maturity, deriving the...

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Bond pricing: In class, we have discussed the pricing of bonds with finite maturity, deriving the bond formula B = C € [ ₁ - + 1 1 (1+r) T P (1+r)T* Here, B is the current bond price, T is the number of periods to maturity, r> 0 is the per-period discount rate, C is the coupon payment, and P is the principal payment due at maturity. A variation of the bond is a perpetuity, which perpetually makes per-period coupon payments and thus never matures. It follows that the price of the perpetuity is B = (a) Consider a growing perpetuity, that makes the payment C after one period, C(1 + g) after two periods, C(1 + g)² after three periods, etc., where 0 < g < r is a constant growth rate. Derive a formula for the value of the growing perpetuity. (b) A very innovative investment banker has decided to introduce a "comet perpetuity," to please astronomers. The asset makes its first payment of USD 2061 at the end of the year 2061 A.D., followed by a payment of USD 2137 at the end of year 2137, and then repeated so that every 76 years a payment is made of the amount equal to the year of the payment (which is also the year that Halley's comet passes our planet). The discount rate is r= 1% per year. It is December 31, 2014. Calculate the value of the comet perpetuity. Bond pricing: In class, we have discussed the pricing of bonds with finite maturity, deriving the bond formula B = C € [ ₁ - + 1 1 (1+r) T P (1+r)T* Here, B is the current bond price, T is the number of periods to maturity, r> 0 is the per-period discount rate, C is the coupon payment, and P is the principal payment due at maturity. A variation of the bond is a perpetuity, which perpetually makes per-period coupon payments and thus never matures. It follows that the price of the perpetuity is B = (a) Consider a growing perpetuity, that makes the payment C after one period, C(1 + g) after two periods, C(1 + g)² after three periods, etc., where 0 < g < r is a constant growth rate. Derive a formula for the value of the growing perpetuity. (b) A very innovative investment banker has decided to introduce a "comet perpetuity," to please astronomers. The asset makes its first payment of USD 2061 at the end of the year 2061 A.D., followed by a payment of USD 2137 at the end of year 2137, and then repeated so that every 76 years a payment is made of the amount equal to the year of the payment (which is also the year that Halley's comet passes our planet). The discount rate is r= 1% per year. It is December 31, 2014. Calculate the value of the comet perpetuity.

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