Page 19 - FINAL CFA SLIDES JUNE 2019 DAY 2

LOS 6.f: Demonstrate the use of a time line in Session Unit 2: The Time Value of Money
modelling and solving time value of money
problems.

Some cash flows don’t start until say Year 4 and extends to Year 6. It would not be uncommon to want to know the PV of this
annuity at the beginning of Year 4, in which case the time index is t = 3 (rather than the usual t = 0).

Loan Payments and Amortization

Example: Loan payment calculation: Annual payments: A company
plans to borrow $50,000 for five years. The company’s bank
will lend the money at a rate of 9% and requires that the loan
be paid off in five equal end-of-year payments. Calculate the
amount of the payment that the company must make in order
to fully amortize this loan in five years.

• N = 5; I/Y = 9; PV = –50,000;
• CPT → PMT = $12,854.62 (five equal instalments)

Note: FV = 0 (as the loan will be fully paid-off/amortized after the five payments have been made).

Example: Loan payment calculation: Quarterly payments: Using the loan described in the preceding example, determine
the payment amount if the bank requires the company to make quarterly payments.

Answer:
• N = 5 × 4 = 20; I/Y = 9 / 4 = 2.25; PV = –50,000;
• CPT → PMT = $3,132.10