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Advanced Financial Management · Securitization

Securitization Numerical Problems for CA Final AFM

Updated 5 October 2026 · Fact-checked

Securitization numericals ask you to work out what a pool of receivables pays, what investors will pay for it, and who gains. List the pool's yearly cash flows, discount them at the investors' required yield to get the certificate price, compare it with face value for premium or discount, then compute SPV profit and the originator's cost of funds.

Understand Securitization Numerical Problems

In securitization, an originator (a bank or NBFC) sells a pool of loans or receivables to a Special Purpose Vehicle (SPV). The SPV pays the originator in cash and raises that cash by issuing securities, usually pass through certificates (PTCs), to investors. The pool's collections then flow to the investors.

So every numerical rests on one idea: the pool cash flows are the only source of payment. Interest and principal collected from borrowers, less any fees and expenses, go to the investors. The originator gets cash today instead of waiting for the loans to be repaid.

Investors do not pay face value by default. They pay the present value of the cash flows at the yield they require. If that yield is lower than the pool's interest rate, the PTC sells at a premium. If it is higher, the PTC sells at a discount. The SPV's gain or loss is the gap between what it raises and what it pays the originator, less its expenses.

For the originator, the question is: what did this funding cost? You compare the cash it receives today with the cash it gives up later, and find the rate that equates them. That rate is the effective cost of funds. Compare it with the originator's normal borrowing rate to judge whether securitization pays.

Key rules to remember

Interest on pool in a period
Interest = Opening outstanding principal × Interest rate
Use the opening balance of that period. Principal repaid reduces the base for the next period.
Pool cash flow for a period
Collection = Principal repaid + Interest collected
Deduct servicing fee or SPV expenses only if the question says they come out of the collections.
Equal instalment on a loan pool
Instalment = P × r ÷ [1 − (1 + r)^(−n)]
Use when the pool is repaid in equal instalments. Interest each period is opening balance × r; principal is instalment minus interest.
Price of a PTC
Price = Σ [Cash flow to investors in year t ÷ (1 + y)^t]
y is the investors' required yield. Pass-through cash flows are the ones actually paid to investors.
Premium or discount
Premium (Discount) = Issue price − Face value of PTC
Positive means premium. Negative means discount.
SPV profit
SPV profit = Proceeds from PTCs − Price paid to originator − SPV expenses
If all collections are passed to investors, the SPV's profit comes only from this gap.
Spread on a pool
Spread = Pool interest rate − PTC coupon rate − Servicing and other costs (as % of pool)
Use when the SPV or originator keeps the excess interest.
Originator's cost of funds
Net cash received today = Σ [Cash paid out in year t ÷ (1 + r)^t]; solve for r
Solve by trial and interpolation. Include any fees the originator pays or any amount it keeps back.

How to solve Securitization Numerical Problems questions

Use the same sequence for any securitization sum. Write each step in a table so partial marks are easy to award.

  1. 1Read the question and identify the originator, the SPV, the pool size, the pool interest rate, the repayment pattern and the investors' required yield.
  2. 2Build the pool schedule: opening balance, interest, principal repaid and closing balance for each period. Use equal principal, equal instalments or bullet repayment as the question states.
  3. 3Compute the collection for each period (principal plus interest). Deduct servicing fee, SPV expenses or credit enhancement only if the question says to.
  4. 4Identify the cash flow actually passed to investors. Under pass through, it is the collection less deductions. If the PTC has its own coupon, compute it on the PTC's face value.
  5. 5Discount the investor cash flows at the required yield to get the PTC price. Compare with face value to state the premium or discount.
  6. 6Compute SPV profit: PTC proceeds less the price paid to the originator less expenses.
  7. 7Compute the originator's cost of funds. Take cash received today, then the cash flows it gives up. Find the rate that equates them using two trial rates and interpolation.
  8. 8State the conclusion in one line, such as whether the PTC is at a premium or discount, or whether securitization is cheaper than the originator's bank borrowing.

Quickest way: One-table method

When to use it: Use when the pool has 2 to 4 periods and the question asks for price, premium or discount, and SPV profit together.

  1. Make one table with columns: Year, Opening, Principal, Interest, Collection, Discount factor, PV.
  2. Fill the Principal column first. Equal principal over n years is pool ÷ n.
  3. Compute Interest as opening × rate, then Collection, then the PV column. Add the PV column for the price.
  4. Subtract face value for the premium or discount, then subtract the SPV's purchase price and expenses for its profit.
  5. For cost of funds, try two rates 1% apart so that one gives a PV above the cash received and the other below. Interpolate.

Common mistakes in Securitization Numerical Problems

  • Charging interest on the original pool every year instead of on the outstanding balance.

    Students copy the first year's interest across when principal is being repaid.

    Fix: Always compute interest as opening balance × rate. Update the balance after each repayment.

  • Discounting at the pool's interest rate instead of the investors' required yield.

    Both rates appear in the question and look alike.

    Fix: The pool rate builds the cash flows. The investor yield discounts them. Underline both in the question.

  • Getting the sign of premium and discount reversed.

    Students compare face value with price in the wrong order.

    Fix: Always use Price − Face value. A positive result is a premium.

  • Counting SPV profit as the full premium and ignoring expenses.

    The question mentions expenses in a later line and the student misses them.

    Fix: Write the SPV profit formula in full and tick off each item against the question before you finish.

  • Calculating cost of funds as a simple percentage of the discount.

    It looks quicker and works for a one-year bullet.

    Fix: For multi-period flows, find the rate at which the PV of outflows equals the cash received. Use interpolation and show both trial rates.

  • Deducting servicing fee or expenses from the investors' cash flows when the question says the originator bears them separately.

    Students assume every cost comes from the pool.

    Fix: Check who bears each cost. Reduce the pool collections only for costs paid out of them.

Worked examples

Example 1

A finance company (originator) has a pool of loans of ₹30 crore, repayable in 3 equal annual principal instalments of ₹10 crore each, with interest at 12% p.a. on the outstanding balance, paid annually. The SPV buys the pool at par for ₹30 crore and issues pass through certificates of ₹30 crore face value. All collections are passed to investors, who require a yield of 10% p.a. SPV expenses are ₹0.20 crore, paid at the start. Calculate the PTC issue price, the premium or discount, and the SPV's profit.

Show the solution
  1. Year 1: opening ₹30 crore. Interest = 30 × 12% = ₹3.60 crore. Collection = 10 + 3.60 = ₹13.60 crore.
  2. Year 2: opening ₹20 crore. Interest = 20 × 12% = ₹2.40 crore. Collection = 10 + 2.40 = ₹12.40 crore.
  3. Year 3: opening ₹10 crore. Interest = 10 × 12% = ₹1.20 crore. Collection = 10 + 1.20 = ₹11.20 crore.
  4. Discount at 10%: Year 1 = 13.60 ÷ 1.10 = 12.3636. Year 2 = 12.40 ÷ 1.21 = 10.2479. Year 3 = 11.20 ÷ 1.331 = 8.4147.
  5. Issue price = 12.3636 + 10.2479 + 8.4147 = ₹31.03 crore (rounded to two decimals).
  6. Premium = 31.03 − 30.00 = ₹1.03 crore.
  7. SPV profit = PTC proceeds 31.03 − purchase price 30.00 − expenses 0.20 = ₹0.83 crore.

Answer: PTC issue price ₹31.03 crore; premium ₹1.03 crore; SPV profit ₹0.83 crore. The PTCs sell at a premium because the pool rate of 12% is higher than the investors' required yield of 10%.

Example 2

An originator sells a pool of receivables of ₹20 crore to an SPV for ₹19.20 crore cash. The pool earns 12% p.a. interest, paid annually for 2 years, with the principal repaid in one lump sum at the end of year 2. The SPV passes all collections to investors. Calculate the originator's approximate effective cost of funds.

Show the solution
  1. Cash received today by the originator = ₹19.20 crore.
  2. The pool collections the originator gives up: Year 1 = 20 × 12% = ₹2.40 crore. Year 2 = 2.40 + 20.00 = ₹22.40 crore.
  3. Set 19.20 = 2.40 ÷ (1 + r) + 22.40 ÷ (1 + r)².
  4. Try 14%: 2.40 ÷ 1.14 = 2.1053 and 22.40 ÷ 1.2996 = 17.2361. Total = 19.3414, which is above 19.20.
  5. Try 15%: 2.40 ÷ 1.15 = 2.0870 and 22.40 ÷ 1.3225 = 16.9376. Total = 19.0246, which is below 19.20.
  6. Interpolate: r = 14% + [(19.3414 − 19.20) ÷ (19.3414 − 19.0246)] × 1% = 14% + (0.1414 ÷ 0.3168) × 1% = 14% + 0.446% ≈ 14.45%.
  7. Check at 14.45%: 2.40 ÷ 1.1445 = 2.0970 and 22.40 ÷ 1.30988 = 17.1008. Total = ₹19.1978 crore, which is close to 19.20.

Answer: The originator's effective cost of funds is about 14.45% p.a. If its normal bank borrowing costs less than this, securitization is the more expensive source of funds, unless it also brings benefits such as removing the loans from its balance sheet.

Exam tips

  • Write the source of every cash flow in your table. Examiners give marks for the schedule even when the final answer slips.
  • Read twice who bears the servicing fee and SPV expenses. This one line changes the investor cash flows and the SPV profit.
  • Round discount factors to four decimals, and state your rounding. ICAI-style answers usually allow small differences from rounding.
  • End with one line of interpretation: premium or discount and why, or whether the cost of funds is above or below bank borrowing.
  • If a question gives defaults or credit enhancement, adjust the pool collections first, then continue with the same steps.

Practice questions from Securitization

Securitization Numerical Problems in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Securitization Numerical Problems: frequently asked questions

Do I discount PTC cash flows at the pool rate or the investor yield?

Discount at the yield the investors require. The pool interest rate is used only to build the cash flows. If the two rates are equal, the PTC prices at face value.

How do I know whether the PTC is at a premium or a discount?

Compute the issue price and subtract the face value. A positive result is a premium and a negative result is a discount. A premium arises when the investors' required yield is below the pool's rate.

How is SPV profit calculated in securitization sums?

SPV profit is the proceeds from issuing PTCs less the price paid to the originator for the pool, less SPV expenses. If the question has other items, such as a fee retained by the SPV, include them. Check who bears each cost before you finalise.

How do I find the originator's cost of funds?

Take the net cash the originator receives today and the cash flows it gives up later. Find the rate that equates their present values using two trial rates and interpolation. Compare that rate with the originator's usual borrowing cost.