Borrowing, Depreciation, Taxes in Cash Flow Problems

Borrowing, Depreciation, Taxes in Cash Flow Problems H. Scott Matthews 12-706 / 19-702 /73-359 Lecture 4

Theme: Cash Flows • Streams of benefits (revenues) and costs over time => “cash flows” • This is our focus for next few classes • We need to know what to do with them in terms of finding NPV of projects • Different perspectives: private and public • We will start with private since its easier • Why “private..both because they are usually of companies, and they tend not to make studies public • Cash flows come from: operation, financing, taxes

Without taxes, cash flows simple • A = B - C • Cash flow = benefits - costs • Or.. Revenues - expenses

Notes on Tax deductibility • Reason we care about financing and depreciation: they affect taxes owed • For personal income taxes, we deduct items like IRA contributions, mortgage interest, etc. • Private entities (eg businesses) have similar rules: pay tax on net income • Income = Revenues - Expenses • There are several types of expenses that we care about • Interest expense of borrowing • Depreciation (can only do if own the asset) • These are also called ‘tax shields’

Goal: Find Cash Flows after taxes • Master equation conceptually: • CFAT = -equity financed investment + gross income - operating expenses + salvage value - taxes + (debt financing receipts - disbursements) + equity financing receipts • Where “taxes” = Tax Rate * Taxable Income • Taxable Income = Gross Income - Operating Expenses - Depreciation - Loan Interest - Bond Dividends • Most scenarios (and all problems we will look at) only deal with one or two of these issues at a time

After-tax cash flows • Dt= Depreciation allowance in t • It= Interest accrued in t • + on unpaid balance, - overpayment • Qt= available for reducing balance in t • Wt= taxable income in t; Xt= tax rate • Tt= income tax in t • Yt= net after-tax cash flow

Equations • Dt= Depreciation allowance in t • It= Interest accrued in t • Qt= available for reducing balance in t • So At = Qt - It • Wt= At-Dt -It (Operating - expenses) • Tt= Xt Wt • Yt= A*t - Xt Wt (pre tax flow - tax) OR • Yt= At + At - Xt (At-Dt -It)

Investment types • Debt financing: using a bank or investor’s money (loan or bond) • DFD:disbursement (payments) • DFR:receipts (income) • DFI: portion tax deductible (only non-principal) • Equity financing: using own money (no borrowing)

Why Finance? • Time shift revenues and expenses - construction expenses paid up front, nuclear power plant decommissioning at end. • “Finance” is also used to refer to plans to obtain sufficient revenue for a project.

Borrowing • Numerous arrangements possible: • bonds and notes (pay dividends) • bank loans and line of credit (pay interest) • municipal bonds (with tax exempt interest) • Lenders require a real return - borrowing interest rate exceeds inflation rate.

Issues • Security of loan - piece of equipment, construction, company, government. More security implies lower interest rate. • Project, program or organization funding possible. (Note: role of “junk bonds” and rating agencies. • Variable versus fixed interest rates: uncertainty in inflation rates encourages variable rates.

Issues (cont.) • Flexibility of loan - can loan be repaid early (makes re-finance attractive when interest rates drop). Issue of contingencies. • Up-front expenses: lawyer fees, taxes, marketing bonds, etc.- 10% common • Term of loan • Source of funds

Sinking Funds • Act as reverse borrowing - save revenues to cover end-of-life costs to restore mined lands or decommission nuclear plants. • Low risk investments are used, so return rate is lower.

Recall: Annuities (a.k.a uniform values) • Consider the PV of getting the same amount ($1) for many years • Lottery pays $A / yr for n yrs at i=5% • ----- Subtract above 2 equations.. ------- • When A=1 the right hand side is called the “annuity factor”

Uniform Values - Application • Note Annual (A) values also sometimes referred to as Uniform (U) .. • $1000 / year for 5 years example • P = U*(P|U,i,n) = (P|U,5%,5) = 4.329 • P = 1000*4.329 = $4,329

Borrowing • Sometimes we don’t have the money to undertake - need to get loan • i=specified interest rate • At=cash flow at end of period t (+ for loan receipt, - for payments) • Rt=loan balance at end of period t • It=interest accrued during t for Rt-1 • Qt=amount added to unpaid balance • At t=n, loan balance must be zero

Equations • i=specified interest rate • At=cash flow at end of period t (+ for loan receipt, - for payments) • It=i * Rt-1 • Qt= At + It • Rt= Rt-1 + Qt <=>Rt= Rt-1 + At + It • Rt= Rt-1 + At + (i * Rt-1)

Annual, or Uniform, payments • Assume a payment of U each year for n years on a principal of P • Rn=-U[1+(1+i)+…+(1+i)n-1]+P(1+i)n • Rn=-U[((1+i)n-1)/i] + P(1+i)n • Uniform payment functions in Excel • Same basic idea as earlier slide

Example • Borrow $200 at 10%, pay $115.24 at end of each of first 2 years • R0=A0=$200 • A1= -$115.24, I1=R0*i = (200)*(.10)=20 • Q1=A1 + I1 = -95.24 • R1=R0+Qt = 104.76 • I2=10.48; Q2=-104.76; R2=0

Various Repayment Options • Single Loan, Single payment at end of loan • Single Loan, Yearly Payments • Multiple Loans, One repayment

Tax Effects of Financing • Companies deduct interest expense • Bt=total pre-tax operating benefits • Excluding loan receipts • Ct=total operating pre-tax expenses • Excluding loan payments • At= Bt- Ct = net pre-tax operating cash flow • A,B,C: financing cash flows • A*,B*,C*: pre-tax totals / all sources

Notes • Mixed funds problem - buy computer • Below: Operating cash flows At • Four financing options (at 8%) in At section below

Further Analysis (still no tax) • MARR (disc rate) equals borrowing rate, so financing plans equivalent. • When wholly funded by borrowing, can set MARR to interest rate

Effect of other MARRs (e.g. 10%) • ‘Total’ NPV higher than operation alone for all options • All preferable to ‘internal funding’ • Why? These funds could earn 10% ! • First option ‘gets most of loan’, is best

Effect of other MARRs (e.g. 6%) • Now reverse is true • Why? Internal funds only earn 6% ! • First option now worst

Bonds • Done similar to loans, but mechanically different • Usually pay annual interest only, then repay interest and entire principal in yr. n • Similar to financing option #3 in previous slides • There are other, less common bond methods

Depreciation • Decline in value of assets over time • Buildings, equipment, etc. • Accounting entry - no actual cash flow • Systematic cost allocation over time • Main emphasis is to reduce our tax burden • Government sets dep. Allowance • P=asset cost, S=salvage,N=est. life • Dt= Depreciation amount in year t • Tt= accumulated (sum of) dep. up to t • Bt= Book Value = Undep. amount = P - Tt

Simple example • Firm: $500k revenues, $300k expense • Depreciation on equipment $20k • No financing, and tax rate = 50% • Yt= At + At - Xt (At-Dt -It) • Yt=($500k-$300k)+0-0.5($200k-$20k) • Yt= $110k

Depreciation Example • Simple/straight line dep: Dt= (P-S)/N • Equal expense for every year • $16k compressor, $2k salvage at 7 yrs. • Dt= (P-S)/N = $14k/7 = $2k • Bt= 16,000-2t, e.g. B1=$14k, B7=$2k • Salvage Value is an investing activity that is considered outside the context of our income tax calculation • If we end up selling asset for salvage value, no further tax implications • If we end up selling asset for higher than salvage value, we may pay additional taxes since we received depreciation expense benefits (but we will generally ignore this since its not the focus of the course)

Accelerated Dep’n Methods • Depreciation greater in early years • Sum of Years Digits (SOYD) • Let Z=1+2+…+N = N(N+1)/2 • Dt= (P-S)*[N-(t-1)]/Z, e.g. D1=(N/Z)*(P-S) • D1=(7/28)*$14k=$3,500, D7=(1/28)*$14k • Declining balance: Dt= Bt-1*r (where r is rate) • Bt=P*(1-r)t,Dt= P*r*(1-r)t-1 • Requires us to keep an eye on B • Typically r=2/N - aka double dec. balance

Ex: Double Declining Balance • Could solve P(1-r)N = S (find nth root) t Dt Bt 0 - $16,000 1 (2/7)*$16k=$4,571.43 $11,428.57 2 (2/7)*$11,428=$3265.31 $8,163.26 3 $2332.36 $5,830.90 4 $1,665.97 $4,164.93 5 $1,189.98 $2,974.95 6 $849.99 $2,124.96 7 $607.13** $1,517.83**

Notes on Example • Last year would need to be adjusted to consider salvage, D7=$124.96 • We get high allowable depreciation ‘expenses’ early - tax benefit • We will assume taxes are simple and based on cash flows (profits) • Realistically, they are more complex

First Complex Example • Firm will buy $46k equipment • Yr 1: Expects pre-tax benefit of $15k • Yrs 2-6: $2k less per year ($13k..$5k) • Salvage value $4k at end of 6 years • No borrowing, tax=50%, MARR=6% • Use SOYD and SL depreciation

Results - SOYD • D1=(6/21)*$42k = $12,000 • SOYD really reduces taxable income!

Results - Straight Line Dep. • NPV negative - shows effect of depreciation • Negative tax? Typically treat as credit not cash back • Projects are usually small compared to overall size of company - this project would “create tax benefits”

Let’s Add in Interest - Computer Again • Price $22k, $6k/yr benefits for 5 yrs, $2k salvage after year 5 • Borrow $10k of the $22k price • Consider single payment at end and uniform yearly repayments • Depreciation: Double-declining balance • Income tax rate=50% • MARR 8%

Single Repayment • Had to ‘manually adjust’ Dt in yr. 5 • Note loan balance keeps increasing • Only additional interest noted in It as interest expense

Uniform payments • Note loan balance keeps decreasing • NPV of this option is lower - should choose previous (single repayment at end).. not a general result

Leasing • ‘Make payments to owner’ instead of actually purchasing the asset • Since you do not own it, you can not take depreciation expense • Lease payments are just a standard expense (i.e., part of the Ct stream) • At= Bt -Ct ; Yt= At - At Xt • Tradeoff is lower expenses vs. loss of depreciation/interest tax benefits

Borrowing, Depreciation, Taxes in Cash Flow Problems