Corporate Finance Lecture 4

Topics covered Inflation in capital budgeting Inflation in capital budgeting –Interest rate and inflation rate –Discounting with inflation Investment with unequal lives Investment with unequal lives

Inflation and capital budgeting Interest rates and inflation Interest rates and inflation –The effect of inflation: The time value of money is deflated by inflation. –Real interest rate vs. nominal interest rate

Inflation Be consistent in how you handle inflation! Be consistent in how you handle inflation! –Use nominal interest rates to discount nominal cash flows. –Use real interest rates to discount real cash flows. –Notice the treatment of depreciations in the two approaches: Depreciation is a nominal number!

Inflation and capital budgeting Approximation Approximation –Real interest rate ≈ Nominal interest rate – Inflation rate –The approximation is reasonably accurate when the interest rate and the inflation rate are low. –Example. Monarchy of Gerberovia has a norminal interest rate of 300% and inflation rate of 280%. (1+300%)/(1+280%)-1=5.26% (1+300%)/(1+280%)-1=5.26% 300%-280%=20% 300%-280%=20%

Inflation Example You own a lease that will cost you $8,000 this year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?

Inflation Example - nominal figures

Inflation Example - real figures

Cash flows and Discount rates: An example year 012 Capital Expenditure 1,210 Revenue (real) 1, Cash expenses (real) Depreciation (straight line) Inflation rate =10% Norminal rate =15.5%

Discount with the real rate Year 012 Cap. Exp Revenue Expenses Depreciation Income bf tax Tax Income af tax NCF

Discount with the real rate Year 012 Cap. Exp Revenue Expenses Depreciation605/1.1605/1.1^2 Income bf tax Tax Income af tax NCF

Discount with the real rate Year 012 Cap. Exp Revenue Expenses Depreciation605/1.1605/1.1^2 Income bf tax Tax Income af tax NCF

Discount with the real rate Year 012 Cap. Exp Revenue Expenses Depreciation605/1.1605/1.1^2 Income bf tax Tax400*40%500*40% Income af tax NCF

Discount with the real rate Year 012 Cap. Exp Revenue Expenses Depreciation605/1.1605/1.1^2 Income bf tax Tax400*40%500*40% Income af tax NCF

Discount with the real rate Year 012 Cap. Exp Revenue Expenses Depreciation605/1.1605/1.1^2 Income bf tax Tax400*40%500*40% Income af tax NCF Real rate= (1+15.5%)/(1+1.10)-1=5%

Discount with the real rate Year 012 Cap. Exp Revenue Expenses Depreciation605/1.1605/1.1^2 Income bf tax Tax400*40%500*40% Income af tax NCF NPV / /1.05^2

Discount with the real rate Year 012 Cap. Exp Revenue Expenses Depreciation605/1.1605/1.1^2 Income bf tax Tax400*40%500*40% Income af tax NCF NPV / /1.05^2 NPV=268

Discount with the nominal rate Year 012 Cap. Exp Revenue1900* *1.1^2 Expenses950* *1.1^2 Depreciation Income bf tax Tax Income af tax NCF

Discount with the nominal rate Year 012 Cap. Exp Revenue1900* *1.1^2 Expenses950* *1.1^2 Depreciation Income bf tax Tax Income af tax NCF

Discount with the nominal rate Year 012 Cap. Exp Revenue1900* *1.1^2 Expenses950* *1.1^2 Depreciation Income bf tax Tax Income af tax NCF

Discount with the nominal rate Year 012 Cap. Exp Revenue1900* *1.1^2 Expenses950* *1.1^2 Depreciation Income bf tax Tax440*40%605*40% Income af tax NCF

Discount with the nominal rate Year 012 Cap. Exp Revenue1900* *1.1^2 Expenses950* *1.1^2 Depreciation Income bf tax Tax440*40%605*40% Income af tax NCF

Discount with the nominal rate Year 012 Cap. Exp Revenue1900* *1.1^2 Expenses950* *1.1^2 Depreciation Income bf tax Tax440*40%605*40% Income af tax NCF

Discount with the nominal rate Year 012 Cap. Exp Revenue1900* *1.1^2 Expenses950* *1.1^2 Depreciation Income bf tax Tax440*40%605*40% Income af tax NCF NPV / /1.155^2

Discount with the nominal rate Year 012 Cap. Exp Revenue1900* *1.1^2 Expenses950* *1.1^2 Depreciation Income bf tax Tax440*40%605*40% Income af tax NCF NPV / /1.155^2 NPV=268

Investments of unequal lives So far, the NPV rule has been our rule- of-thumb. So far, the NPV rule has been our rule- of-thumb. However, there are situations when the NPV rule is not sufficient. However, there are situations when the NPV rule is not sufficient. E.g. when investments under decision have different lengths of life. E.g. when investments under decision have different lengths of life.

Investments of unequal lives Date Machine01234 A B Discount rate=0.1

Investments of unequal lives Date Machine01234 A NPV A B NPV B

Investments of unequal lives Date Machine01234 A NPV A / /1.1^2-120/1.1^3 B NPV B

Investments of unequal lives Date Machine01234 A NPV A / /1.1^2-120/1.1^ B NPV B

Investments of unequal lives Date Machine01234 A NPV A / /1.1^2-120/1.1^ B NPV B / /1.1^2-100/1.1^3-100/1.1^4

Investments of unequal lives Date Machine01234 A NPV A / /1.1^2-120/1.1^ B NPV B / /1.1^2-100/1.1^3-100/1.1^

Investments of unequal lives Date Machin e A NPV A / /1.1^2-120/1.1^ B NPV B / /1.1^2-100/1.1^3-100/1.1^ NPV rule will suggest Machine A because it has a lower NPV of costs……But, is this correct?

Investments of unequal lives The NPV rule does not consider the time that each machine will last. The NPV rule does not consider the time that each machine will last. –Machine A is cheaper but only last for three years. –Machine B is more costly but last for one more year. Therefore, it is necessary to compare the cost on a per year basis. Therefore, it is necessary to compare the cost on a per year basis.

Investments of unequal lives Date Machine01234 A NPV A Annuity A C1C1C1 B NPV B Annuity B C2C2C2C2

Investments of unequal lives Annuity Annuity A: =C1* A: =C1*C1=798/2.4869= B: =C2* C2=916.99/3.1699= C1>C2, it is cheaper to buy machine B