# MACRS depreciation schedule

### Quiz

Question 1)

What is the minimum lease payment that would make purchasing a computer system and writing a 6-year lease contract on it?  The price of the computer system is \$175,000, it is a five-year asset for depreciation purposes, it has a residual value of \$3,000, it requires \$500 maintenance per year, the cost of capital is 9%, and the corporate tax rate is 40%.(Note:  MACRS rates for Years 1 to 6 are 0.20, 0.32, 0.19, 0.12, 0.11 and 0.06.)

Question 2)

Dakota Trucking Company (DTC) is evaluating a potential lease for a truck with a 4-year life that costs \$40,000 and falls into the MACRS 3-year class.  If the firm borrows and buys the truck, the loan rate would be 10%.The truck will be used for 4 years, at the end of which time it will be sold at an estimated residual value of \$10,000.  If DTC buys the truck, it would purchase a maintenance contract that costs \$1,000 per year, payable at the end of each year.  The lease terms call for a \$10,000 lease payment (4 payments total) at the beginning of each year.  DTC’s tax rate is 40%.  Should the firm lease or buy?

Question 3)

What is IPO underpricing?

Use the following information for questions 4 and 5

A company is planning to go public. Currently, the pre-IPO value of the firm’s equity is \$95 million, the number of outstanding shares is 3.5 million, the company need to raise \$17 million, and the floatation cost of new equity is 12%.

Question 4)

Calculate the gross proceeds needed from an IPO given the above information.

Question 5)

Part a

What is the post-IPO equity value?

Part b

What is the offer price?

Solution

Q1

 Year 0.00 1.00 2.00 3.00 4.00 5.00 6.00 Initial cost (-ve. number) -175000.00 Maintenance costs etc (-ve. number) -500.00 -500.00 -500.00 -500.00 -500.00 -500.00 -500.00 Tax shield on costs 200.00 200.00 200.00 200.00 200.00 200.00 200.00 5-year MACRS depreciation schedule 0.20 0.32 0.19 0.12 0.11 0.06 Depreciation tax shield 14000.00 22400.00 13300.00 8400.00 7700.00 4200.00 Total -175300.00 13700.00 22100.00 13000.00 8100.00 7400.00 3900.00 PV -175300.00 12568.81 18601.13 10038.39 5738.24 4809.49 2325.44 Total PV -121218.50 PMT 27022.00

 Cost of capital % 9.00 Tax rate % 40.00

 Year 0 1 2 3 4 Cost of new truck 40000 3-year MACRS depreciation schedule % 0.33 0.45 0.15 0.07 Lost depn. tax shield -5280.00 -7200.00 -2400.00 -1120.00 Lease payment -10000.00 -10000.00 -10000.00 -10000.00 -10000.00 Tax shield of lease payment 4000.00 4000.00 4000.00 4000.00 4000.00 Cash flow of lease 34000.00 -11280.00 -13200.00 -8400.00 -7120.00 After-tax borrowing rate % 6.00 PV lease cash flows 34000.00 -10641.51 -11747.95 -7052.80 -5639.71 NPV of lease -1081.97 Note: Tax rate % 40 Borrowing rate % 10

Q2(ii)

 Year 0 1 2 3 4 Amount borrowed at year-end 35081.00 25905.86 14260.21 6715.82 -1.23 Interest paid -3508.10 -2590.59 -1426.02 -671.58 Interest tax shield 1403.24 1036.23 570.41 268.63 Interest paid after tax -2104.86 -1554.35 -855.61 -402.95 Principal repaid -9175.14 -11645.65 -7544.39 -6717.05 Net cash flow of equivalent loan 35081.00 -11280.00 -13200.00 -8400.00 -7120.00 Note: Tax rate % 40.00 Borrowing rate % 10.00

Question 1)

What is the minimum lease payment that would make purchasing a computer system and writing a 6-year lease contract on it?  The price of the computer system is \$175,000, it is a five-year asset for depreciation purposes, it has a residual value of \$3,000, it requires \$500 maintenance per year, the cost of capital is 9%, and the corporate tax rate is 40%.(Note:  MACRS rates for Years 1 to 6 are 0.20, 0.32, 0.19, 0.12, 0.11 and 0.06.)

Minimum lease payment that would make purchasing a computer system and writing a 6-year lease contract on it is \$27022.

 Year 0 1 2 3 4 5 6 Initial cost -175000.00 Maintenance costs -500.00 -500.00 -500.00 -500.00 -500.00 -500.00 -500.00 Tax shield on costs 200.00 200.00 200.00 200.00 200.00 200.00 200.00 5-year MACRS depreciation schedule 0.20 0.32 0.19 0.12 0.11 0.06 Depreciation tax shield 14000.00 22400.00 13300.00 8400.00 7700.00 4200.00 Total -175300.00 13700.00 22100.00 13000.00 8100.00 7400.00 3900.00 PV -175300.00 12568.81 18601.13 10038.39 5738.24 4809.49 2325.44 Total PV -121218.50 PMT 27022.00 Cost of capital % 9.00 Tax rate % 40.00

Question 2)

Dakota Trucking Company (DTC) is evaluating a potential lease for a truck with a 4-year life that costs \$40,000 and falls into the MACRS 3-year class.  If the firm borrows and buys the truck, the loan rate would be 10%.The truck will be used for 4 years, at the end of which time it will be sold at an estimated residual value of \$10,000.  If DTC buys the truck, it would purchase a maintenance contract that costs \$1,000 per year, payable at the end of each year.  The lease terms call for a \$10,000 lease payment (4 payments total) at the beginning of each year.  DTC’s tax rate is 40%.  Should the firm lease or buy?  (Note:  MACRS rates for Years 1 to 4 are 0.33, 0.45, 0.15, and 0.07.)

Since, in the case of lease NPV is negative DTC is better off buying the truck. The lease payments are contractual obligations like the principal and interest payments on secured debt. Thus, we can think of the incremental lease cash flows in years 1 through 4 as the “debt service” of the lease. Table 2 shows a loan with exactly the same debt service as the lease. The initial amount of the loan is \$35081. It costs exactly the same to service a loan that brings an immediate inflow of 35081 as it does to service the lease, which brings in only 34000. That is why we say that the lease has a net present value of 34000 – 35081 = –\$1081. If DTC leases the truck rather than raising an equivalent loan \$1081.97 less in DTC’s bank account

 0 1 2 3 4 Cost of new truck 40000 3-year MACRS depreciation schedule % 0.33 0.45 0.15 0.07 Lost depn. tax shield -5280.00 -7200.00 -2400.00 -1120.00 Lease payment -10000.00 -10000.00 -10000.00 -10000.00 -10000.00 Tax shield of lease payment 4000.00 4000.00 4000.00 4000.00 4000.00 Cash flow of lease 34000.00 -11280.00 -13200.00 -8400.00 -7120.00 After-tax borrowing rate % 6.00 PV lease cash flows 34000.00 -10641.51 -11747.95 -7052.80 -5639.71 NPV of lease -1081.97 Tax rate % 40 Borrowing rate % 10

Question 3)

What is IPO underpricing?

Underpricing happens when the Initial Public Offering is listed below its market value. Whenever the stock is first traded, if its trading price is higher than the offer price of the stock, it is considered to be a case of underpricing.

Use the following information for questions 4 and 5

A company is planning to go public. Currently, the pre-IPO value of the firm’s equity is \$95 million, the number of outstanding shares is 3.5 million, the company need to raise \$17 million, and the floatation cost of new equity is 12%.

Question 4)

Calculate the gross proceeds needed from an IPO given the above information.

 Pre-IPO value of equity = \$95 million Target net proceeds = \$17.00 million Number of existing shares = 3.5  million

Gross required proceeds    = Target Net proceeds/(1 – floatation cost)

=\$17/(1-0.12) million

=\$19.318 million

Question 5)

Part a

What is the post-IPO equity value?

Post IPO Equity Value = Target Net proceeds + (1 – floatation cost)*Gross Required Proceeds

=\$17million + (1 – 0.12)*\$19.318 million

= \$112 million

Part b

What is the offer price?

Offer Price = VPre-issue/(F NNew + NExisting)

where,

VPre-issue= \$95million

F-cost    = 0.12

NExisting   = 4 million

% of value required by new investors     = Gross Investment / Post IPO Equity value

= (\$19.318million/\$112million)

= 17.25%

NNew          = (% of value reqd. by investors*Existing shares)/(1 – % of value required by new investors)                                                       = (0.1725*4)/(1 – 0.1725)

= 0.73 million

Hence,

Offer Price = (\$95 million)/(0.12 * 0.73million + 4 million)

= \$26.48