Declining GIC ladder

Declining GIC ladders consist of Guaranteed Investment Certificates of varying terms (or maturities). These fixed income ladders provide cash flow over a predetermined period of up to 5 years. The cash flow consists of both interest payments and the principal from maturing GICs: these combine to provide the targeted amounts, which are spent. So by design, there is nothing left in a declining ladder at the end, unlike with a rolling ladder in which the GIC principals are reinvested instead of spent. Declining ladders are also known as one-time ladders or non-rolling ladders.

Declining GIC ladders can be set up to provide any dollar amount at any time, but a typical design provides equal payments once per year, and this is the focus of this article. In that case, if the declining ladder is set up at a single time using a lump sum, the result is the economic equivalent of buying a term certain annuity.

Applications of a declining GIC ladder providing equal amounts every year include:

• financing education and living costs during a university or other degree;
• providing extra retirement income while waiting for government benefits (OAS) or pensions (CPP/QPP) to start at the regular age, or at voluntarily delayed ages, i.e. bridging an income gap.

This article focusses on ladder design using a lump sum to provide equal payments at the beginning of the year. Variations include providing equal payments at the end of the year, providing unequal (e.g., rising) amounts, or setting up the ladder in advance; these are briefly mentioned.

Payments at the beginning of the year

Suppose you want to provide $20 000 a year, for 5 years, with payments at the beginning of each year, starting immediately, using a lump sum. The first $20k (year 0) can simply be transferred from your investment account to a chequing account (for immediate spending) or to a HISA (to spend it progressively over the year). Then you put enough money in a 1 year GIC, a 2 year GIC, a 3 year GIC and a 4 year GIC to provide the subsequent payments. But how do you calculate the amounts to place in each GIC maturity? It depends if you are using a registered or a non-registered account.

Using a registered account: compounding GICs

When using a registered account (such as RRSPs, RESPs, ...), compounding GICs -- which only pay the earned interest upon maturity -- can be used. This simplifies the math, as each yearly payment comes from a single GIC. For readers familiar with bonds, compounding GICs are mathematically similar to zero-coupon bonds (strip bonds) in that there are no interest payments (in bond parlance, "coupons") recieved before maturity. Therefore, the zero-coupon bond formula will be used below.

Step 1: input values

First, decide on the cash flow required at the beginning of each year. The example calls for $20k a year; this is what each GIC must be worth at maturity, including principal and interest. So the purchase price (principal) will be less than $20k for each GIC.

Then, gather the relevant interest rates from your discount brokerage or online bank. Suppose those are 3.7%, 4.0%, 4.3%, and 4.6% for terms of 1 to 4 years.

Step 2: calculate the principal of each GIC

The zero-coupon bond formula with annual compounding (e.g., ) is used to calculate the present value (purchase price or "principal") of each compounding GIC:

present value (purchase price) = F / (1 + r)^t

where F is the "face value" in bond terms (for a compounding GIC, the value at maturity including principal and interest), r is the interest rate, and t is the time to maturity in years.

In our example, the 4 year GIC providing $20k at maturity would cost :

purchase price = $20 000 / (1+0.046)⁴ = $16 707

In Excel, you can use the =POWER(number;power) function for the denominator; here the “number” is (1+0.046) and the "power" (exponent) is 4.

At maturity, the investor would get $16 707 of principal back, plus $3293 of interest, for a total of $20k. No interest would be received on this GIC during earlier years.

The purchase prices of the other compound GICs are calculated in the same way. The order of the calculations does not matter: each rung in the ladder is independent.

Step 3: results

We get the following ladder:

Year	Interest rate	Value at maturity (principal + interest)	GIC purchase price (principal)
0	N/A	$20 000	N/A (transfer $20k out)
1	3.7%	$20 000	$19 286
2	4.0%	$20 000	$18 491
3	4.3%	$20 000	$17 627
4	4.6%	$20 000	$16 707
Total	N/A	$100 000	$92 112

The early rungs cost more because the money is invested for fewer years, and to a much lesser extent because of the normally (upwards) sloping yield curve in the example.

Longer declining ladders could be created using strip bonds (a.k.a. zero-coupon bonds).

Using a non-registered account: non-compounding GICs

In non-registered accounts, compounding GICs are not recommended due to the tax treatment of accrued interest. In short, interest would be taxed every year, even though no money might have yet been received. Instead, use non-compounding GICs that pay interest regularly: you get taxed on what you actually earn. In the following example, yearly interest payments are assumed, to facilitate calculations.

Step 1: input values

Suppose that the desired payments and the relevant interest rates are as above: we want $20k of cash flow per year, and GICs of one to four years yield 3.7%, 4.0%, 4.3%, and 4.6%.

Step 2: calculate the longest-dated GIC

Unlike when using compounding GICs, here the order of calculations matters. Start with the last (longest-dated) GIC in the ladder, here the 4 year. The question is: what is the purchase price of a non-compounding GIC for which the final year payment (one year of interest plus the principal) equals $20k? The formula is:

purchase price of last GIC = final year payment / (1 + r)

In our example:

purchase price (principal) of 4 year GIC = $20 000 / (1+0.046) = $19 120

This is similar to the zero-coupon bond formula above, but without the exponent in the denominator because we care only about the final year of interest for this non-compounding GIC, when calculating its purchase price. At maturity, the 4 year GIC will supply $19 120 of principal repayment and $880 of final interest.

Step 3: calculate the other GICs

The four year GIC will also pay $880 of interest in years 3, 2 and 1. We need to take that into account when we calculate how much of the 3 year GIC to buy. The formula becomes:

purchase price = (total payment wanted – interest from longer terms) / (1 + r)

In our example, for the 3 year GIC:

purchase price = ($20 000 – $880) / (1 + 0.043) = $18 332

For the 2 year GIC, we take into account interest from the 4 year and 3 year GICs, and so on.

Step 4: results

This yields the following ladder of non-compounding GICs:

Time (years) →	0	1	2	3	4
Initial spending	20000
4 year GIC: interest		880	880	880	880
4 year GIC: principal repayment					19120
3 year GIC: interest		788	788	788
3 year GIC: principal repayment				18332
2 year GIC: interest		705	705
2 year GIC: principal repayment			17627
1 year GIC: interest		629
1 year GIC: principal repayment		16998
Total amount received	20000	20000	20000	20000	20000

The table represents cash flows from the ladder and is presented with the longest-dated GIC at the top, to show the order in which the calculations are performed. The total purchase price is $92 078, slightly less than in the example with the registered account. Note how the longer the term, the more money is required, because the 4 year GIC supplies cash flow over four years, and the interest is spent progressively instead of compounded.

Variations

In the examples above, equal amounts are provided at the beginning of each year, using a lump sum. Other configurations are possible.

Payments at the end of the year

If, for some reason, payments are required at the end of the year, then the initial immediate payment to a bank account ($20k in the previous examples) is not made. Instead, the first payment will come from the one year GIC. If 5 years of cash flow is wanted, a five year GIC can be added to the end of the ladder.

In the case of a non-registered account where non-compounding GICs are used, start by calculating the amount of 5 year GIC to purchase, then the 4 year, and so on.

Increasing amounts

The declining ladder can be set up to provide payments that increase over time, for example to account for anticipated inflation. Pick a rate of increase, say 3%. The target payments become $20 000, then $20 600 ($20k*1.03), then $21 218 ($20.6k*1.03), and so on. Here is the result for a registered account, with payments at the end of the year:

The Excel formula in cell B11 is =B6/POWER(1+B7;B4), which can then be stretched to cell F11 to calculate the purchase amounts for the four other GICs.

Setting it up in advance

All of the cases examined so far involved converting a lump sum into a stream of payments that start immediately or at the end of the first year. But the investor might instead want set up the GIC ladder in advance of the period during which payments will be needed. Reasons for doing this include keeping the money in a safe place, or accumulating it progressively.

In such a case, the basic idea is to initially set up a rolling GIC ladder. This can be done on a single day (for example, buy equal amounts of 1, 2, 3, 4, 5 year GICs). The rolling ladder can also be set up progressively over time, for example by adding a rung (likely a 5 year GIC) every year until the ladder is complete. Maturing GICs are renewed (reinvested) until the money is actually needed, and then the rolling ladder becomes a declining ladder.

In terms of how much to invest in each maturity, the target payments can be used, to keep things simple. The ladder will eventually provide more than the target payments due to interest. But that extra interest might compensate, more or less, for inflation and taxes if applicable.

See also

• Annuities