STAT2032 Chap.4 Loans and Capital Budgeting
Loans and Capital Budgeting
Loans and projects are both equations of value, but their questions point in different directions. Loan work asks how a fixed advance is divided among interest and principal across repayments, and it checks the outstanding balance at a precise instant. Capital budgeting asks whether a project creates value at a required discount rate and how that decision differs from solving for an internal rate of return.
This chapter joins payment calculation, prospective and retrospective balances, amortisation schedules, net present value and IRR while keeping the governing cash-flow signs visible.
An amortisation row begins with the outstanding balance, adds interest for the payment period, applies the repayment and closes with a new balance. Interest plus principal reduction must equal the repayment.
A balance immediately after a payment excludes that instalment from the prospective stream; a balance immediately before it still includes the amount due. Prospective valuation discounts remaining repayments, while retrospective valuation accumulates the original advance and subtracts accumulated past payments.
Agreement between the two is an independent timing check.
Project analysis uses the same valuation mechanics with a decision focus. NPV measures money value created at a chosen required return. IRR solves for a rate at which that value becomes zero, and discounted payback records when the cumulative discounted position recovers its outlay.
These measures need not rank alternatives identically when scale or timing differs. Write the cash-flow signs first, use NPV for the value decision at the relevant hurdle, and interpret IRR as a break-even rate rather than as an amount of value. Multiple sign changes also warn that more than one internal rate may exist.
What this chapter covers
- 01
Level loan repayments
- 02
Interest and principal splits
- 03
Prospective loan balances
- 04
Retrospective loan balances
- 05
Net present value
- 06
Internal rate of return
Worked example · free
Calculate a payment and remaining balance
- 2At advance, 15000 = R[1 - (1.02)^(-5)]/0.02.
- 1Solving gives the quarterly repayment R = $3,182.38.
- 1Immediately after payment two, three payments remain.
- 1The prospective balance is R[1 - (1.02)^(-3)]/0.02 = $9,177.60.
- 1The balance is below the original advance after two repayments, which is directionally reasonable.
Key terms
- Amortisation schedule
- A period-by-period record dividing each repayment into interest and principal and updating the loan balance.
- Prospective method
- A balance calculation based on the present value of repayments remaining after the balance date.
- Net present value
- The discounted value of project inflows less project outflows at the required return.
- Internal rate
- A discount rate that makes the net present value of a specified cash-flow sequence equal to zero.
Loans and Capital Budgeting FAQ
Why do loan payments contain changing principal amounts?
Interest for a period is charged on the opening balance. With a level repayment, the remainder reduces principal. As the balance falls, the next interest charge falls, leaving more of the unchanged payment for principal. This is why the interest portion declines and the principal portion rises across an ordinary amortisation schedule.
Should I use a prospective or retrospective balance?
Choose the side with fewer or simpler cash flows. The prospective method values remaining repayments, while the retrospective method accumulates the original advance and subtracts accumulated past repayments. They agree when evaluated at the same instant using the same rate. Disagreement usually signals a before-payment versus after-payment timing error.
Why can NPV and IRR lead to different project rankings?
NPV measures value created at the required return in money units. IRR is a rate internal to the project cash-flow pattern. Different project scale, timing, reinvestment assumptions or non-conventional sign changes can make rate rankings conflict with value rankings. For a decision at a specified required return, NPV directly measures the added value.
What does immediately after a repayment mean?
Interest for the period has already been charged and the repayment has already reduced the balance. A prospective calculation therefore includes only later instalments. Immediately before the repayment is a different instant and still contains the amount then due, so confusing the two positions shifts the balance by one payment.
Exam move
Build one complete amortisation row by hand: opening balance, interest, repayment, principal reduction and closing balance. Then propagate the logic to later rows and verify that the final balance approaches zero apart from rounding. Calculate selected balances by both prospective and retrospective methods at exactly the same instant.
In capital budgeting, write out the sign sequence before choosing a rule, and graph or tabulate NPV at several discount rates so the IRR is seen as a zero crossing rather than a calculator label. Keep the required return separate from the solved internal rate. For mutually exclusive projects, explain the decision in value terms rather than reporting only a percentage.
Round repayments carefully because using a rounded payment inside multiple later periods can create a small terminal residual that belongs to rounding, not to the valuation method.
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