FIN435 • Course Hub Spring 2026

Goal: price bonds correctly, interpret yields, and explain interest-rate risk and credit/call risk.

• Bond price = PV(coupons) + PV(par) discounted at the required yield (YTM as IRR).
• Price–yield inverse: yield ↑ ⇒ price ↓; yield ↓ ⇒ price ↑.
• Premium vs discount: coupon rate > YTM ⇒ premium; coupon rate < YTM ⇒ discount.
• Current yield = annual coupon ÷ price (income only). YTM includes price pull-to-par + timing.
• Duration (rate risk): higher duration ⇒ bigger % price move for a given Δy (1st-order sensitivity).
• Callable bonds: upside is capped when rates fall (call risk; negative convexity region).
• Risk premiums: Treasuries mainly term/liquidity; corporates add default + liquidity premiums.

Common exam traps: confusing coupon rate vs YTM; treating current yield as “total return”; forgetting call risk limits price gains; assuming higher coupon ⇒ higher duration (often the opposite).

Goal: decide whether a project adds value and choose the best project when projects compete for the same capital.

• Net Present Value (NPV): the gold-standard decision rule. NPV = Σ [CF_t / (1 + r)^t] − Initial Cost. If NPV > 0, the project increases shareholder wealth.
• Internal Rate of Return (IRR): the discount rate that makes NPV = 0. Accept if IRR > required return, but IRR can mislead when cash flows are nonnormal or projects are mutually exclusive.
• Modified IRR (MIRR): fixes key IRR problems by assuming positive cash flows are reinvested at the cost of capital, not at IRR. MIRR gives only one solution and is easier to interpret.
• Payback Period: how long it takes to recover the initial investment. Useful for liquidity/risk intuition, but it ignores time value and cash flows after payback.
• Discounted Payback: improves payback by discounting cash flows first, but still ignores later cash flows after the cutoff.
• Profitability Index (PI): PI = PV of future cash flows / Initial Cost. Helpful under capital rationing, but for normal decisions NPV is still preferred.

When rankings conflict:

• Independent projects: accept every project with NPV > 0.
• Mutually exclusive projects: choose the project with the higher NPV, even if it has the lower IRR.
• Why conflict happens: differences in scale (project size) or timing (early vs late cash flows).

Crossover rate:

• The crossover rate is the discount rate where two projects have the same NPV.
• To find it, subtract one project’s cash flows from the other to form an incremental cash flow stream, then compute the IRR of the difference.
• If the required return is below the crossover rate, one project is preferred; if it is above, the other may be preferred.

Excel reminders:

• =NPV(rate, CF1:CFn) + CF0  (do not include initial cost inside the NPV range)
• =IRR(CF0:CFn)
• =MIRR(CF0:CFn, finance_rate, reinvest_rate)

Common exam traps: forgetting to subtract the initial investment in NPV, choosing the higher IRR instead of the higher NPV for mutually exclusive projects, missing the possibility of multiple IRRs with nonnormal cash flows, and confusing MIRR with IRR.