FIN509 • Chapter 9 — Capital Budgeting (MBA)

Chapter 9 — Capital Budgeting (MBA)

NPV • IRR • MIRR • PI • Payback • Discounted Payback — with syntax cards, mini calculators, worked examples, and homework preloads.

Intro

Capital budgeting evaluates long-term projects by turning future cash flows into today’s value or by finding required returns. For this course, focus on:

NPV (gold standard for value creation)
IRR & MIRR (rates of return; MIRR fixes IRR’s reinvestment assumption)
PI (useful when capital is rationed)
Payback / Discounted Payback (speed of recovery; screening tools)

Tip: For Excel, cash flows usually go in rows/columns. Make sure signs are right (CF0 < 0, later CFs generally > 0), and that periods are equally spaced.

Excel Syntax (Quick Cards)

NPV

=NPV(rate, value1, value2, ...)

Values occur at period ends
Add CF0 separately: NPV(...) + CF0

IRR

=IRR(values, [guess])

Array must include CF0 and all cash flows
Guess optional; helps convergence

MIRR

=MIRR(values, finance_rate, reinvest_rate)

Needs at least one negative and one positive CF
Uses explicit reinvest & finance rates

Profitability Index (PI)

PI = 1 + NPV / |CF0| (or PV of future CFs ÷ |CF0|)

Payback

Time to recover initial outlay (undiscounted). Discounted payback uses present values.

Mini Calculators

Inputs

Enter CF0 (negative) and subsequent CFs (comma-separated). Example: -800, 350, 350, 350

Discount rate (as %) Cash flows (CSV incl. CF0)

Outputs

NPV:

IRR:

MIRR (fin=reinv=rate):

PI:

Payback (yrs):

Disc. Payback (yrs):

Manual formulas used

NPV = Σ CF_t / (1+r)^t
IRR solves NPV(IRR)=0 (bisection search here)
MIRR: grow positives at reinvest rate, discount negatives at finance rate, then annualize
PI: 1 + NPV / |CF0|
Payback = years until cumulative CF ≥ 0 + fraction of final year
Discounted payback uses PVs

In-Class Example — Single Project

WACC = 11%; CFs: CF0 = -800; CF1=350; CF2=350; CF3=350.

Expected (from your notes): NPV ≈ 55.30; IRR ≈ 14.93%; PI ≈ 1.069; Payback ≈ 2.286 yrs; Disc. Payback ≈ 2.72 yrs.

Multi-Project Choice — IRR vs NPV

WACC = 7.5%. Mutually exclusive projects S and L:

Year	0	1	2	3	4
S	-1,100	550	600	100	100
L	-2,700	650	725	800	1,400

Reminder: “True value” is measured by NPV. IRR can rank differently when cash flow scale/timing differs.

Non-Conventional Cash Flows (Multiple IRRs)

CFs: CF0 = -90,000; CF1=132,000; CF2=100,000; CF3=-150,000. Required return = 15%.

Multiple sign changes ⇒ multiple IRRs possible (here: ~10.11% and ~42.66%).
Use NPV at required return (15%) or use MIRR to avoid ambiguity.

Method Summary (When to Use What)

Approach	Description	Pros	Cons	Use Cases
NPV	PV of CFs − initial	Direct value add; uses time value	Needs discount rate; CF estimates matter	Primary decision metric
IRR	Rate making NPV=0	Intuitive % return	Multiple IRRs; reinvest at IRR assumption	Supplement for conventional CFs
MIRR	IRR with explicit rates	Fixes reinvest assumption	More inputs	Comparing projects with reinvest policy
PI	PV future CFs ÷ \|CF0\|	Ranks under capital rationing	Not for mutually exclusive picks	Budget-constrained portfolios
Payback / DPB	Time to recover outlay	Simple; liquidity focus	Ignores value after recovery	Screening / risk-averse settings

Quick Quiz

Click to check answers.

Homework (Due with Final)

Q1

CF0 = -20,000; CFs: 8,000; 4,000; 3,000; 5,000; 10,000. r = 10%.

Payback ≈ 4.00 yrs
NPV ≈ 2,456.74
IRR ≈ 14.55%
PI ≈ 1.12

Q2

CF0 = -60,000; CFs: 25,000; 24,000; 13,000; 12,000; 11,000. r = 15%.

Payback ≈ 2.85 yrs
NPV ≈ 764.27
IRR ≈ 15.64%
PI ≈ 1.013 (Accept)

Q3 (Mutually Exclusive)

One-year A vs B at 10%: Choose B (NPV 227.27 vs 72.73).
3-year A vs B at 10%: Mutually exclusive ⇒ choose A (NPV ≈ 758.83 > 616.45). Independent ⇒ choose both. Crossover ≈ 21.01%.

Resources

Note: Calculators here are for instruction; for official work, verify in Excel/approved tools.