what is question and answe

Let's work through the problem together. Here's what we need to find:

Question: The amount of the lease$-$equivalent loan is closest to:

To solve this problem, we need to calculate the lease$-$equivalent loan using the given information.

Given:

Price of the internet server: $$2\mathrm{.}5$ million

Marginal tax rate for TigerCorp: $15\%$

Accelerated depreciation: $50\%,30\%,20\%$ over three years

Cost of debt for TigerCorp: $6\%$

Cost of equity: $10\%$

Annual lease payments: $$1\mathrm{.}4$ million for three years

Steps:

Calculate the depreciation tax shield:

Depreciation for Year $1$: $50\%$ of $$2\mathrm{.}5$ million $=$ $$1\mathrm{.}25$ million

Depreciation for Year $2$: $30\%$ of $$2\mathrm{.}5$ million $=$ $$0\mathrm{.}75$ million

Depreciation for Year $3$: $20\%$ of $$2\mathrm{.}5$ million $=$ $$0\mathrm{.}5$ million

Tax shield each year $=$ Depreciation $*$ Tax rate

Calculate the present value $($PV$)$ of the depreciation tax shield:

PV for each year, discounted at the cost of debt $(6\%)$

Calculate the present value of the lease payments:

Annual lease payment: $$1\mathrm{.}4$ million

PV of an annuity of $$1\mathrm{.}4$ million for three years at $6\%$

Calculate the lease$-$equivalent loan:

Total cost of owning $($net of tax shield$)$ should be equivalent to the PV of lease payments

Let's go step by step. How do you think we should start?

do everything

Alright, let's break down the steps and calculate each part to find the lease$-$equivalent loan.

Step $1$: Calculate the Depreciation Tax Shield

Depreciation:

Year $1$:

$50$

$\%$

$\backslash$times

$

$2\mathrm{.}5$

$$million

$=$

$

$1\mathrm{.}25$

$$million

$50\%\backslash$times $$2\mathrm{.}5$million$=$$$1\mathrm{.}25$million

Year $2$:

$30$

$\%$

$\backslash$times

$

$2\mathrm{.}5$

$$million

$=$

$

$0\mathrm{.}75$

$$million

$30\%\backslash$times $$2\mathrm{.}5$million$=$$$0\mathrm{.}75$million

Year $3$:

$20$

$\%$

$\backslash$times

$

$2\mathrm{.}5$

$$million

$=$

$

$0\mathrm{.}5$

$$million

$20\%\backslash$times $$2\mathrm{.}5$million$=$$$0\mathrm{.}5$million

Tax Shield:

Tax rate: $15\%$

Year $1$ Tax Shield:

$

$1\mathrm{.}25$

$$million

$\backslash$times

$0\mathrm{.}15$

$$1\mathrm{.}25$million$\backslash$times $0\mathrm{.}15$

Year $2$ Tax Shield:

$

$0\mathrm{.}75$

$$million

$\backslash$times

$0\mathrm{.}15$

$$0\mathrm{.}75$million$\backslash$times $0\mathrm{.}15$

Year $3$ Tax Shield:

$

$0\mathrm{.}5$

$$million

$\backslash$times

$0\mathrm{.}15$

$$0\mathrm{.}5$million$\backslash$times $0\mathrm{.}15$

Step $2$: Calculate the Present Value $($PV$)$ of the Depreciation Tax Shield

Cost of debt $($discount rate$)$: $6\%$

Using the formula for present value:

$$

$$

$=$

$$

$$

$($

$1$

$+$

$$

$)$

$$

PV$=$

$(1+$r$)$

t

CF

$$

Step $3$: Calculate the Present Value of the Lease Payments

Using the formula for the present value of an annuity:

$$

$$

annuity

$=$

$$

$\backslash$times

$($

$1$

$$

$($

$1$

$+$

$$

$)$

$$

$$

$$

$)$

PV

annuity

$$

$=$C$\backslash$times $($

r

$1(1+$r$)$

$$t

$$

$)$

where:

$$

C is the annual lease payment: $$1\mathrm{.}4$ million

$$

r is the discount rate: $6\%$

$$

t is the number of years: $3$

Let's calculate these values step$-$by$-$step using Python and SymPy$.$

First, we'll calculate the tax shields and their present values. Then, we'll calculate the present value of the lease payments and finally find the lease$-$equivalent loan.

Let's do these calculations.

Here are the results of our calculations:

Total Present Value of the Depreciation Tax Shields:

$

$339$

$,$

$982\mathrm{.}84$

$$339,982\mathrm{.}84$

Present Value of the Lease Payments:

$

$3$

$,$

$742$

$,$

$216\mathrm{.}73$

$$3,742,216\mathrm{.}73$

Step $4$: Calculate the Lease$-$Equivalent Loan

The lease$-$equivalent loan is the present value of the lease payments minus the total present value of the tax shields.

Lease$-$equivalent$$loan

$=$

PV$$of$$lease$$payments

$$

Total$$PV$$of$$tax$$shields

Lease$-$equivalent$$loan$=$PV$$of$$lease$$payments$$Total$$PV$$of$$tax$$shields

Let's calculate this:

Lease$-$equivalent$$loan

$=$

$

$3$

$,$

$742$

$,$

$216\mathrm{.}73$

$$

$

$339$

$,$

$982\mathrm{.}84$

Lease$-$equivalent$$loan$=$$$3,742,216\mathrm{.}73$$$339,982\mathrm{.}84$

I'll do this calculation for you. $$

The lease$-$equivalent loan amount is approximately $$3,402,233\mathrm{.}89.$

Now let's compare this with the given options:

a$.$ $$2\mathrm{.}43$ million

b$.$ $$3\mathrm{.}37$ million

c$.$ $$2\mathrm{.}55$ million

d$.$ $$3\mathrm{.}58$ million

The closest option is:

b$.$

$

$3\mathrm{.}37$

$$3\mathrm{.}37$ million

Does this make sense to you? If you have any questions or need further clarification, feel free to ask! $$

type everything in the picture l send

Sure, here's the text from the image you provided:

TigerCorp plans to add a new internet server, which has a price of $$2\mathrm{.}5$ million. TigerCorp expects that the internet server will be worthless after three years. The marginal tax rate for TigerCorp is $15\%.$ The tax authority approves that the new internet server can use the accelerated depreciation: TigerCorp can depreciate $50\%,30\%,$ and $20\%$ of the value of the internet server in the next three years. Assume that the cost of debt for TigerCorp is $6\%,$ and its cost of equity is $10\%.$ If TigerCorp uses this internet server through a true tax lease for three years, instead of direct purchasing, the annual lease payments will be $$1\mathrm{.}4$ million. The amount of the lease$-$equivalent loan is closest to:

Select one:

a$.$ $$2\mathrm{.}43$ million

b$.$ $$3\mathrm{.}37$ million

c$.$ $$2\mathrm{.}55$ million

d$.$ $$3\mathrm{.}58$ million