Question

In: Finance

3. A 5-year project requires an initial investment of $28 million. It generates an annual cash...

3. A 5-year project requires an initial investment of $28 million. It generates an annual cash flow of $9 million. The unlevered cost of equity is 20%. A loan of $22.5 million at a rate of 10%. Principal will be repaid in a lump sum when project ends. However, the lender will extend the loan for only three years. The firm’s tax rate is 30%. Calculate the project’s adjusted present value.

Solutions

Expert Solution

> Formula

Adjusted Present Value = NPVL + PVD

Where NPVL is the net present value of cash flows calculated using the unlevered cost of equity (also called ungeared cost of equity, unlevered cost of capital or opportunity cost of capital).

PVD is the present value of tax shield. Tax savings in any one period can be calculated as follows:

Tax Savings = T × rd × D

Where T is the tax rate, rd is the pre-tax cost of debt and D is the total value of debt.

Use the gross cost of debt as the appropriate discount rate for tax savings.

> Calculation

  • Calculation of NPVL

Present Value of cash inflow = Annual Inflow * PVAF( Unlevered rate, Number of years )

                                          = 9 Million * PVAF (20%, 5)

                                          = 9 Million * [ 1/1.20 + 1/1.202 +.....+ 1/1.205 ]

                                          = 9 Million * 2.9906

                                          = $ 26915509.26

Present Value of Cash outflow = $ 28 mn

NPV = Present Value of cash inflow - Present Value of Cash outflow

       = 26915509.26 - 28000000

       = $ - 10,84,490.74

                                          

  • Calculation of PVD
Year Tax Savings Present Value
1

22.5 Mn * 10% * 30%

= 675000

675000 / 1.1

= 613636.36
2

22.5 Mn * 10% * 30%

= 675000

675000 / (1.10)2

= 557851.24
3

22.5 Mn * 10% * 30%

= 675000

675000 / (1.10)3

= 507137.49
1678625.09
  • Adjusted Present Value Calculation

APV = $ - 10,84,490.74 + 16,78,625.09

        = $ 594134.35 Answer

Hope you understand the solution.

jeff jeffy answered 1 year ago
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