Valuing British Perpetuities: A 6% Interest Rate Analysis

 Problem:

Solution:

The value of a perpetuity is given by the formula:

$$\mathrm{<span\; style="font-family:\; arial;"><span\; style="font-size:\; medium;">P</span></span>}\mathrm{<span\; style="font-family:\; arial;"><span\; style="font-size:\; medium;">V</span></span>}=\frac{\mathrm{<span\; style="font-size:\; medium;">C</span>}}{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; arial;">r</span></span><span\; style="font-family:\; arial;\; text-align:\; justify;"></span>}}$$

where:

• PV = Present value of the perpetuity

• $C$ = Annual interest (coupon payment)

• r = Discount rate (interest rate)

(a) Value of the 4% Perpetuity

• Coupon Payment: £4 per year
• Interest Rate: 6% (0.06 in decimal form)

$$PV = \frac{4}{0.06} = 66.67$$

So, the value of the 4% perpetuity is £66.67.

(b) Value of the 2.5% Perpetuity

• Coupon Payment: £2.50 per year
• Interest Rate: 6% (0.06 in decimal form)

$$PV = \frac{2.50}{0.06} = 41.67$$

So, the value of the 2.5% perpetuity is £41.67.