Problem 1. With interest rates so low, some investors have considered replacing bond investments with stable dividend paying stocks. First we'll look at a bond.
a. ONT 3.5 June/2/2043 is a bond issued by the Province of Ontario. The 3.5% coupon is paid semi-annually on June 2 and December 2 (i.e. $1.75 per $100). Set up a column of dates and cash flows in Excel and manually discount them by a rate that you can adjust. (Pretend it is December 2 right now so we don't have to deal with accrued)
b. What discount rate gets you a Present Value at the trading price of $105?
c. Check your answer with the XNPV function. (Put a 0 cash flow for December 2, 2015 to hack the formula).
d. What is the present value of the final $101.75 cash flow (that is ~28 years from now)?
Problem 2. Choice Properties REIT equity is a candidate for a "bond surrogate" because it pays a stable distribution supported by collecting rent on grocery stores.
a. What is the current distribution (per share) of Choice Properties REIT? How often do they pay?
b. Assuming the dividend never changes, set up a cash flow table for the perpetual dividend and discount the cash flows (back to Dec 2 again). How do you deal with infinity here? Find a discount rate to get the present value close to the current trading price. Compare to the "dividend yield": annual dividend divided by price.
c. Reprogram your model to include a growth rate. Assume 3% annual growth (rent increases and development). What's the discount rate to get close to the current trading price? Compare to the constant case.
d. Compare these exercises to the annuity, perpetuity and growing perpetuity in the textbook. Do the textbook formulas work?
e. Interest rate risk. Suppose the Fed raises rates more than expected and all discount rates jump by 1%. What's the percentage price loss on
i. The Ontario long bond
ii. The constant-distribution Choice REIT (g=0%)
iii. The growing Choice REIT (g=3%)
Problem 3. IRR vs NPV.
a. Read this paper for the main idea https://papers.ssrn.com/sol3/papers.cfm?abstract_id=522722
b. Verify the numerical results in Table 2. Repeat for a 10% discount rate.
c. In your own words, compare the usefulness of the IRR rule and NPV rule for capital budgeting decisions. Explain how they are connected and outline how to give meaning to the imaginary roots of the IRR equation.
4. After-tax yield on bonds. Most bonds right now trade at a lower market yield than their coupon. Therefore, the price is more than par (why?). Real examples of bonds with live prices here https://www.ftse.com/products/FTSETMX/Home/LiveFixed
(I will post a spreadsheet to help with this problem)
a. Build a spreadsheet with the semi-annual coupon cash flows. Given a purchase price you can compute the yield using an IRR (and check it with the YIELD function). Use COUPNCD to get the first date in the cash flow table. Convention is yields are expressed as 2 times the semiannual rate. So use 2*[sqrt(1+IRR)-1]
b. The new Alberta tax rates for incomes over $300k are 44% on income and 22% on capital gains (check this). Assume you are in that bracket and make a new column of after tax cash flows. On the first coupon, you don't pay tax on the accrued that you paid. And you get a tax bonus at maturity based on the capital loss.
c. Find a bond that has a negative after-tax yield! (Recall yield is IRR). Recommend an alternative with similar risk, but better tax treatment.