Question

If you had two investments to choose from, one a perpetuity that pays $100/year forever, or the other, a bond that pays interest of $100/year for 30 years, then pays back the $1000 principal, which one would you choose?

Please show calculation

Answer 1

We will choose the investment which has higher present value

Let's say discount rate is 10%

Present value of perpetuity is = c/r

= 100/10% = 1000

Value of the bonds is also 1000 when market rate is equal to yield

Now let us assume market interest rate to be 9%

Pv of perpetuity is = 100/9% = 1111.11

Value of bond at 9% discount rate

= 100(PVIFA 9% 30Y) + 1000/(1.09)^30

= 100(10.2737) + 75.37

= 1102.7

Conclusion

If market interest rate is below 10% perpetuity has higher present value so perpetuity will be choosen

If market interest rate is 10% we are indifferent to both options

Where rate is above 10% we choose bonds because bonds have more pv than perpetuity