Question

Assume that AT&T’s pension fund managers are considering two alternative securities as investments: (1) Security Z (for zero intermediate year cash flows), which costs $422.41 today, pays nothing during its 10-year life, and then pays $1,000 at the end of 10 years or (2) Security B, which has a cost today of $500 and pays $74.50 at the end of each of the next 10 years.

Which security would you recommend be purchased and why?

Security Z:

Security B:

Answer 1

The security which provides highest rate of return per annum will be recommeded to purchase.
Security Z
We can use the present value of sum formula to calculate the rate of return provided by Security Z.
Present value of sum = F x [1/(1+r)^n]
Present value of sum = present value of security Z = $422.41
F = Future value of security = $1000
r = rate of return = ?
n = no.of years = 10
422.41 = 1000 x [1/(1+r)^10]
0.42241 = [1/(1+r)^10]
r = 0.09
Rate of return provided by Security Z = 9%
Security B
We can use the present value of annuity formula to calculate the rate of return provided by Security B
Present value of annuity = A x {[1-(1+r)^-n]/r}
Present value of annuity = present value of security = $500
A = yearly payment = $74.50
r = rate of return = ?
n = no.of years = 10
500 = 74.50 x {[1-(1+r)^-10]/r}
6.711409 = [1-(1+r)^-10]/r
r = 0.08
Rate of return provided by Security B = 8%
I would recommend Security Z be purchased as it provides highest rate of return per year.