On Feb. 5, 2000, ScotiaMcLeod, offered some Government of Canada stripped coupon

Question

On Feb. 5, 2000, ScotiaMcLeod, offered some Government of Canada stripped coupons. Each coupon represented a promise to pay $100 to the holder at the maturity date on Feb. 5, 2020, but investors would receive nothing until then. Investors paid ScotiaMcLeod $29.19 for each coupon. What rate was the Government paying to borrow money?On Feb. 5, 2000, ScotiaMcLeod, offered some Government of Canada stripped coupons. Each coupon represented a promise to pay $100 to the holder at the maturity date on Feb. 5, 2020, but investors would receive nothing until then. Investors paid ScotiaMcLeod $29.19 for each coupon. What rate was the Government paying to borrow money?

Explanation / Answer

Today’s value = (Annual interest * Sum of PVF) + Maturity date Value * PVF for 20th

29.19 = 0 + 100 (PVF for 20th year)

PVF for 20th year = 29.19/100

PVF for 20th year = .2919

Now we can check this PVF in Table. Following PVF are taken from table:

At 7 % = .2584

At 6% = .3118

Gov. Rate = X

Rate =

Lower rate + (PVF at lower – PVF at X rate/ PVF at lower rate – PVF at higherRate)* Diff in rates

6+ (.3118-.2919)/(.3118-.2584) * 1

6 + .35

= 6.35% Approx.

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