Strategic Financial Management · Securitization

Numerical Problems on Securitization and Valuation of Pools

Updated 11 October 2026 · Fact-checked

A securitization numerical asks you to value a pool of receivables sold to an SPV. Build the pool's cash flows (instalment, interest, principal, prepayments), deduct servicing fees, then discount the net amounts at the investors' required yield. The result is the price of the pass-through certificates, compared with the pool's outstanding principal.

Understand Numerical Problems on Securitization and Valuation of Pools

In securitization, an originator (a bank or NBFC) sells a pool of loans or receivables to a special purpose vehicle (SPV). The SPV pays for the pool by issuing pass-through certificates (PTCs) to investors. Whatever the borrowers pay is passed on to the investors, after small deductions such as the servicing fee.

So a numerical has two parts. First, you find the cash flows of the pool. Second, you value those cash flows. The pool's cash flows come from the loan terms: coupon rate, tenor and repayment pattern. The value comes from the discount rate, which is the yield investors demand for the risk of the pool, not the rate the borrowers pay.

If investors demand a yield below the pool's interest rate, the PTCs are worth more than the outstanding principal (a premium). If investors demand a higher yield, the PTCs sell at a discount. Always compare your value with the outstanding principal.

Prepayments change the timing. Borrowers pay principal early, so the balance falls faster and later interest is lower. Investors get cash sooner but earn less total interest. In exam problems, the prepayment is usually given as an amount or a percentage of the balance, and you rebuild the schedule from that point.

Credit enhancement (such as a cash collateral or excess spread) and the servicing fee reduce or protect investor cash flows. Read the question for each of these and apply only what is stated.

Key rules to remember

Instalment on a level-payment pool: EMI = P × r ÷ [1 − (1 + r)^−n]; P is the pool principal, r the rate per period, n the number of periods. Use the annuity factor if the question gives one.
Interest and principal split: Interest = Opening balance × r; Principal = Instalment − Interest; Closing balance = Opening balance − Principal − Prepayment; Interest is always on the opening balance after the previous period's prepayment.
Net cash flow to investors: Net flow = Interest + Principal + Prepayment − Servicing fee; Deduct fees and any stated retained amounts. Do not deduct anything the question does not mention.
Value of the PTC / pool: Value = Σ [Net flow(t) ÷ (1 + y)^t]; y is the investors' required yield per period, not the pool's coupon.
Premium or discount: Premium (+) or Discount (−) = Value − Outstanding principal; Value above principal means investors accept a yield lower than the pool coupon.
Single monthly mortality (prepayment rate): SMM = Prepayment ÷ (Opening balance − Scheduled principal); Use only when the question gives a prepayment rate. It applies to the balance after the scheduled principal.
Periodic rate from annual rate: Monthly rate = Annual rate ÷ 12 (nominal); (1 + y)^(1/12) − 1 (effective); Use the convention the question states. Default to the nominal rate ÷ 12 if unspecified.

How to solve Numerical Problems on Securitization and Valuation of Pools questions

Use this order for any pool-valuation question. It keeps the working tidy and each step earns marks.

1Note the pool size, coupon rate, tenor, repayment frequency, investors' required yield, servicing fee and any prepayment or default data.
2Compute the periodic instalment with the annuity formula, unless the question gives the instalment.
3Prepare a schedule: opening balance, interest, principal, prepayment, closing balance for each period.
4Deduct the servicing fee and other stated deductions to get the net cash flow to investors in each period.
5Discount each net flow at the investors' required yield, using the correct periodic rate.
6Add the present values to get the value of the PTCs or the pool.
7Compare with the outstanding principal and state the premium or discount, and give a clear conclusion on price or yield.

Quickest way: Annuity-factor shortcut for a level pool

When to use it: Use when there are no prepayments or fees and the pool pays equal instalments. It saves the full schedule.

Find the instalment: Pool ÷ annuity factor at the pool coupon for n periods.
Multiply this instalment by the annuity factor at the investors' yield for the same n.
That product is the value of the PTC. Compare with the pool principal.
If fees or prepayments are given, switch to the schedule method, because the cash flows are no longer level.

Common mistakes in Numerical Problems on Securitization and Valuation of Pools

Discounting at the pool's coupon rate instead of the investors' required yield.
Both rates appear in the question and the coupon is used to build the schedule.
Fix: Use the coupon only to build cash flows. Use the investors' yield only to discount them.
Calculating interest after a prepayment on the old balance.
Students keep the original schedule and add the prepayment as an extra flow.
Fix: Reduce the closing balance by the prepayment and recompute next period's interest on the new balance. The instalment for later periods also changes if the tenor is unchanged.
Charging the servicing fee on the original pool size.
The fee percentage is read as applying to the whole pool every year.
Fix: Apply it to the opening balance of each period unless the question says otherwise.
Mixing monthly cash flows with an annual discount rate.
The yield is quoted per annum and is used without converting.
Fix: Convert the rate to the same period as the cash flows before discounting.
Ignoring the premium or discount conclusion.
The calculation ends at the present value.
Fix: Always state value minus outstanding principal and what it means for the SPV and investors.
Treating the PTC value as the SPV's profit.
The roles of the originator, SPV and investors get confused.
Fix: The SPV passes the cash flows through. The gain or loss on sale belongs to the originator, measured against the book value of the assets.

Worked examples

Example 1

A bank sells a pool of loans of ₹10,00,000 to an SPV. The loans carry interest at 10% p.a. and are repaid in three equal annual instalments. Investors in the PTCs require a yield of 12% p.a. There are no prepayments or fees. Find the value of the PTCs and the premium or discount. (Annuity factor for 3 years: 10% = 2.48685; 12% = 2.40183.)

Show the solution

Instalment = 10,00,000 ÷ 2.48685 = ₹4,02,115 (approx.).
Value of PTCs = 4,02,115 × 2.40183 = ₹9,65,812 (approx.).
Discount = 9,65,812 − 10,00,000 = −₹34,188.

Answer: The PTCs are worth about ₹9,65,812. They sell at a discount of about ₹34,188 to the outstanding principal, because investors demand 12% against a pool coupon of 10%.

Example 2

An SPV buys a pool of ₹10,00,000 with interest at 12% p.a., repayable in two equal annual instalments. The servicing fee is 1% of the opening balance each year, deducted from collections. At the end of year 1, after the scheduled instalment, borrowers prepay ₹2,00,000. Investors require 15% p.a. Find the value of the PTCs. (Annuity factor for 2 years at 12% = 1.69005.)

Show the solution

Instalment = 10,00,000 ÷ 1.69005 = ₹5,91,698.
Year 1: interest = 12% × 10,00,000 = ₹1,20,000; principal = 5,91,698 − 1,20,000 = ₹4,71,698; closing balance = 10,00,000 − 4,71,698 = ₹5,28,302.
Year 1 fee = 1% × 10,00,000 = ₹10,000. Net flow year 1 = 5,91,698 − 10,000 + 2,00,000 (prepayment) = ₹7,81,698.
Balance after prepayment = 5,28,302 − 2,00,000 = ₹3,28,302.
Year 2: interest = 12% × 3,28,302 = ₹39,396; collection = 3,28,302 + 39,396 = ₹3,67,698. Fee = 1% × 3,28,302 = ₹3,283. Net flow = 3,67,698 − 3,283 = ₹3,64,415.
PV of year 1 = 7,81,698 ÷ 1.15 = ₹6,79,737.
PV of year 2 = 3,64,415 ÷ 1.3225 = ₹2,75,550.
Total value = 6,79,737 + 2,75,550 = ₹9,55,287.

Answer: The PTCs are worth about ₹9,55,287, a discount of about ₹44,713 to the ₹10,00,000 principal, because investors' 15% yield exceeds the 12% pool coupon.

Exam tips

Write the schedule as a small table-style list: opening balance, interest, principal, prepayment, closing. Examiners follow it easily and award method marks even if a figure slips.
Read whether the prepayment comes before or after the scheduled instalment. It changes the interest base.
State your assumption on rate conversion (nominal monthly or effective) in one line when the question is silent.
Close with the premium or discount and a one-line recommendation on whether the price is acceptable to investors.
In MCQs, estimate first: a required yield above the coupon means a value below principal. This removes wrong options fast.

Practice questions from Securitization

Numerical Problems on Securitization and Valuation of Pools in other exams

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

CA FinalSecuritization Numerical Problems

Numerical Problems on Securitization and Valuation of Pools: frequently asked questions

What discount rate do I use for securitized receivables?

Use the yield the PTC investors require, which reflects the risk of the pool. Do not use the borrowers' interest rate unless the question says investors earn exactly that rate.

How do prepayments affect the value of a pool?

They bring principal back earlier and cut later interest. If the investors' yield is below the pool coupon, early return usually lowers value. If it is above the coupon, early return can raise value.

Is the servicing fee deducted before discounting?

Yes. Investors receive collections net of the servicing fee, so you deduct it from each period's collection and then discount the net amount.

How is the SPV discount rate different from the pool rate?

The pool rate is what borrowers pay and is used to build cash flows. The SPV or investor discount rate is the required return of certificate holders and is used to price the PTCs.