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Homework answers / question archive / 1)In a Treasury auction of $2
1)In a Treasury auction of $2.1 billion par value 91-day T-bills, the following bids were submitted: Bidder Bid Amount Price per $100 1 $500 million $99.40 2 $750 million $99.01 3 $1.5 billion $99.25 4 $1 billion $99.36 5 $600 million $99.39 If the Treasury also received $750 million of non-competitive bids, who will receive T-bills and at what price? You must show your calculation, otherwise, your mark will be deducted.
2)
ToneLock Ltd, security experts and lock manufacturers are considering entering into the
production of impenetrable combination safes. The company has called you, their trusted
financial advisor, to recommend whether to proceed with the project. The company tells you
that the cost of the machinery required to manufacture these safes is $560,000, with an
additional $40,000 to install. The machinery will be depreciated straight line on an annual
basis over its entire useful life of 4 years to a salvage value of $30,000. The company also
estimates that the building in which the machine is to be installed requires renovation
expenses of $25,000 if the company is to go ahead with the project, which for tax purposes
will be expensed at the beginning of the project.
The project will generate pre?tax revenues in the first year of $200,000, with revenues
expected to grow at a rate of 20% p.a., thereafter. Pre?tax expenses have been estimated to
be 15% of pre?tax revenues. ToneLock Ltd also believes that they can receive $10,000 for the
machinery at the end of its useful life. Given a required rate of return of 10% p.a. compounded
semi?annually, and a corporate tax rate of 30%, do you recommend that ToneLock Ltd
proceed with this project and commence manufacturing impenetrable safes? Why or why
not? In answering this question, assume the initial investment is made today and cash flows
are received or paid as stated in the question.
1)
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T-bills are sold by Dutch Auction method. |
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Dutch auction price is that auction in which all bids accepted are awarded at same price or same yield. |
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We will calculate cumulative number of T-bills up to which all issue can be sold. |
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Ranking will be made on the basis of Highest price offered. |
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First, all Non-competitive bids for $750 million or 0.75 billion are taken for consideration. |
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Now issue amount left is $2.1 billion -0.75 billion = 1.35 billion |
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Then Bidder 1 bid is Highest $99.40 per $100. So bidder 1 will be awarded Bidded amount of 500 million or $0.50 billion |
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Now issue left is $1.35 billion - 0.5 billon = 0.85 billion |
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Then Bidder 5 bid is Highest $99.39 per $100. So bidder 5 will be awarded $500 Million or 0.50 billion Bidded Amount |
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Now issue left is $0.85 billion - 0.5 billon = 0.35 billion |
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Then Bidder 4 bid is Highest $99.36 per 100. So bidder 4 will be awarded remaining 0.350 billion Last price at which all issue is sold is $9.9.36 per $100 So issue price is 99.36 per $100 or 0.9936 for all bidders. |
So bidder 1 ,5, 4 and non competitive bidders will get it @99.36 per $100 issue price
| Bidder | Bid Amount awarded | Issue Price per 100 |
Total amount paid |
| Non Competitive bids | 0.75 | 0.9936 | 0.7452 |
| 1 | 0.5 | 0.9936 | 0.4968 |
| 5 | 0.5 | 0.9936 | 0.4968 |
| 4 | 0.35 | 0.9936 | 0.34776 |
| Total | 2.1 | 2.08656 |
2)
1) Do you recommend that ToneLock Ltd proceed with the project for manufacturing the safes?
To answer this, we need to find out the viability of the project using various capital budgeting techniques. The widely used capital budgeting techinques are the Net Present Value (NPV) and Internal Rate of Return (IRR). To compute NPV & IRR, we need to determine the cash flows that the project is capable of generating and the Discounting factor.
Step 1: Cash flow generated by the project.
The below table shows the cash flow from the project for the next 4 years.
| Particulars | Year 0 | Year 1 | Year 2 | Year 3 | Year 4 |
| Sales - A | $ 200,000 | $ 240,000 | $ 288,000 | $ 345,600 | |
| Operating expenses @15% of sales - B | $ 30,000 | $ 36,000 | $ 43,200 | $ 51,840 | |
| Depreciation* - C | $ 142,500 | $ 142,500 | $ 142,500 | $ 142,500 | |
| Renovation expenses - D | $ 25,000 | $ - | $ - | $ - | |
| Earnings Before Tax (A-B-C-D) | $ 2,500 | $ 61,500 | $ 102,300 | $ 151,260 | |
| Less: Tax @30% | $ 750 | $ 18,450 | $ 30,690 | $ 45,378 | |
| Profit After Tax | $ 1,750 | $ 43,050 | $ 71,610 | $ 105,882 | |
| Add: Depreciation | $ 142,500 | $ 142,500 | $ 142,500 | $ 142,500 | |
| Add: Renovaion expenses** | $ 25,000 | ||||
| Cash Flow | $ 169,250 | $ 185,550 | $ 214,110 | $ 248,382 | |
| Capital expenditure | $ -600,000 | $ 10,000 | |||
| Building renovation | $ -25,000 | ||||
| Free cash flow | $ -625,000 | $ 169,250 | $ 185,550 | $ 214,110 | $ 258,382 |
Note:
* Depereciation = (Cost of the machine - Salvage value)/Life of the machine = (600,000-30,000)/4 = $142,500.
** Renovation expenses are dedecuted as expenses in the first year for taxation purpose. It is added back while arriving at free cash flow as these expeneses are already considered as outflow in the Year 0.
Step 2: Arriving at the Discounting factor.
The Discounting factor given is 10% compounded semi-annually. We need to convert to the effective annual interest rate as the free cash flows are on annual basis.
Below is the formula to convert the semi-anually compounded interest to effective annual interest.
Effective annual interest rate = [1 + (nominal rate / number of compounding periods)) ^ (number of compounding periods] - 1
Effective annual interest rate = [1+(10%/2)^2]-1 = 10.25% p.a
Step 3 : Calculate NPV.
| Year | Free cash flow | Discounting Factor @10.25% | Present Value |
| Year 0 | $ (625,000) | 1.000 | $ (625,000) |
| Year 1 | $ 169,250 | 0.907 | $ 153,515 |
| Year 2 | $ 185,550 | 0.823 | $ 152,652 |
| Year 3 | $ 214,110 | 0.746 | $ 159,772 |
| Year 4 | $ 258,382 | 0.677 | $ 174,883 |
| NPV | $ 15,822 |
Step 4: IRR
IRR is calculated based on the free cash flow. IRR for this project is 11.34% (computed using excel. Alternatively, it can be calculated using trial and error method).
Conclusion:
ToneLock Ltd, should go ahead with the manufacturing of safes as the NPV is positive and the IRR is more than the required rate of return for the company.
