Final rehearsal: the “never seen” set
◈ 9 cardsSix answer-only items that each chain two modules — a bond bought at one yield and sold at another, CAPM into Gordon, a margin call, a put writer, a Canadian mortgage, an NPER — because that is what “questions you may never have seen” turn out to be.
What “never seen” means
The final's Excel part marks the answer and nothing else, and its hardest items are ones the practice package did not contain. Read them and a pattern appears: each is two lessons chained — the output of one function is an input to the next. Nothing in them is new; the join is. So the method is the same as Lesson 6.6's: read the stem, write the five variables and the function for each step, compute, and check the size of the answer before committing.
Two of the six are solved here in full. Four are yours.
(a) A bond bought at issue and sold early — Module 10 + Module 13
A 6 % semi-annual, $1,000-par, 12-year bond is bought at issue when yields are 5.5 %. Three years later, with 9 years left, yields are 5 % and it is sold. Realised return?
Step 1 — the purchase price. rate = 0.055 ÷ 2 = 0.0275, nper = 24, pmt = 30, fv = 1,000: =-PV(0.0275,24,30,1000) = 1,043.50 (a premium: coupon above yield).
Step 2 — the sale price. Same bond, but fewer periods and a new rate: rate = 0.025, nper = 18: =-PV(0.025,18,30,1000) = 1,071.77. The trap is re-using 24 and 0.0275 — the purchase inputs — for the sale.
Step 3 — the holding-period return (Lesson 13.1), with six coupons of 30 = 180 collected: =(1071.77-1043.50+180)/1043.50 = 0.199583 — 19.96 % over three years.
Step 4 — annualise by the root: =(1+0.199583)^(1/3)-1 = 0.062535 — 6.25 % a year. Above the 5.5 % bought at, because yields fell and the price rose. Size check: a bond bought at 5.5 % whose yield fell should have earned a little more than 5.5 % — it did.
(b) CAPM into Gordon — Module 13 + Module 11
RF 3 %, β 0.9, expected market return 8 %; the share paid D₀ = 2.00 last year and dividends grow at 3 %. Price?
Step 1 — the required return (Lesson 13.4): =0.03+0.9*(0.08-0.03) = 0.075.
Step 2 — the Gordon price (Lesson 11.3), from D₁ = D₀(1 + g): =2.00*1.03/(0.075-0.03) = 2.06 ÷ 0.045 = 45.78. The D₀ trap gives 2.00 ÷ 0.045 = 44.44 — the paper's favourite wrong answer.
Four for you
(c) Margin call — Module 11. 800 shares at 55 on 50 % margin, maintenance 30 %. The loan is 55 × 800 × 0.5 = 22,000 and is fixed; the call price is where equity is 30 % of value: =22000/(800*(1-0.30)). Size check: below 55.
(d) A put writer — Module 12. Wrote a put, K = 60, premium 2.80; at expiry S_T = 54. Per share =2.80-MAX(60-54,0); per contract × 100. Size check: a writer's profit is never above the premium.
(e) A Canadian mortgage — Module 7. 11 — a wrong answer that looks right, which is why the rate conversion is its own cell.
(f) Months to repay — Module 6. $15,000 at 7.2 % compounded monthly, $450 a month: =NPER(0.072/12,-450,15000). Sign: pmt and pv opposite, or #NUM!. Size check: 15,000 ÷ 450 = 33 months with no interest, so a little more than that.
The margin note
On an answer-only paper the one check you get is whether the answer's size is plausible. Write, for each step, the function and its five variables; then ask whether the number is the right order of magnitude and on the right side of the obvious bound. That habit, not any formula, is what the rehearsal is for.