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- May 23, 2018

Solution a). The interest earned and the effective annual rate of interest are calculated as follows. The investment is for 5 years i.e. 20 quarters.

The effective annual rate of intrest is approximately 6.1 %.

Solution 1(b) In this question we need to find out the annuity amount of 7 annuities compounding at 7% for 5 years.

The annuity is due at the end of the year thus it’s an ordinary annuity.

The annuity value is 8750

Solution 1© The present value of the residual value of the machine after 8 years discounted at 8 % will be given as:

Solution 1(d)

9 % yearly rate can be written as .75% (9/12) monthly rate.

Thus to pay 750000 now at i = .0075 in 36 installments, the annuity amount will be calculated as:

As the annuity was due at the start of the year we used the formula for due annuity.

To calculate the outstanding balance after 1 year, we will calculate the value of 750000 after 1 year at 9% and from this value we will subtract the future value of the 12 annuities that would have been paid in a year’s time.

The loan amount of 750000 will be 817500 in a year at 9% rate.

In one year 12 monthly installments of 24270 each, compounding monthly would have yielded 300948.

Thus after one year the outstanding loan will be = 817500 – 300948 = 512552.

Ans 2- Solution to the problem 2 is in the attached excel file.

PBP calculation

Since there are no formulae for PBP and discounted PBP in Excel, These calculations are shown here.

Project A

Discounted

Initial Cost

-1000.0000

Inflow at the end of year 1

250.0000

224.2152

Inflow at the end of year 2

300.0000

241.3079

Inflow at the end of year 3

350.0000

252.4896

Inflow at the end of year 4

400.0000

258.7978

The rate is 11.5%

PBP for project A

Payback in first three years = 250 + 300 + 350 = 900

After year 3 the remaining amount to be recovered = 1000 – 900 = 100

The payback in year 4 = 400

Amount to be recovered in year 4 = 100

The proportion of year 4 to recover 100 = 100 / 400 = .25

Thus PBP = 3+.25 = 3.25 years

Discounted PBP for project A

Since the NPV in four year is negative, the discounted PBP cannot be calculated.

Project B

Project B

Discounted

Initial Cost

-1000.0000

Inflow at the end of year 1

400.0000

358.7444

Inflow at the end of year 2

350.0000

281.5259

Inflow at the end of year 3

300.0000

216.4196

Inflow at the end of year 4

250.0000

161.7486

The rate is 11.5%

PBP for project B

Payback in 2 years = 400 + 350 = 750

Amount to be recovered in the third year = 1000 -750 = 250.

The amount recovered in year 3 = 300

The proportion of the year 3 to recover 250 = 250 / 300 = 5 /6 = .83 years

The PBP for Project = 2+ 0.83 = 2.83 years

Discounted PBP for Project B

Discounted Payback in three years = 856.6

The amount to be recovered in year 4 = 1000 – 856.6 = 143.4

Discounted Payback in year 4 = 161.7

The proportion of year 4 for recovering 143.4 = 143.4 / 161.7 = .88 years

Thus the discounted PBP = 3 + 0.88 = 3.88 years.

Ans 2(b)

If the projects are mutually exclusive we can invest in only one of the projects, thus we need to rank order the projects. In such situations it may so happen that NPV and IIR clash i.e. both give different results, in such a situation NPV takes precedence over IRR as it is more consistent with the wealth maximizing principle. However in this case both NPV and IRR give the same result i.e. Project B is better than project A as only it has positive NPV and only it’s IRR is higher than cost of capital.

If the projects are independent, selection of one project does not affect the selection chances of the other projects. The evaluation of projects is done solely on the basis of their IIR and NPVs.

Going by both the NPV and IRR rules

Project A cannot be undertaken as The NPV is negative ( -23.2) and IRR is also than cost of capital ( 10.48% < 11.5 %).

Project B can be undertaken as it generates positive NPV (18.4) and IRR is also higher than cost of capital (12.44% > 11.5%).

Yes it is better to get large cash flows early and tail off later or to get large cash flows later in the project life cycle because that would offer more money to be reinvested at the earlier stage which will generate more value. Even in these two projects though the sum being returned is same i.e. 1300 but since project B gives larger sums in the initial years it offer higher IRR, MIRR and NPV.

Ans 3

Assumptions:

Depreciation on old machine is calculated considering the book value for next 4 years.

Depreciation on new machine is calculated considering the purchase cost for next four years.

Initial Investment

(a) Initial Investment for the Proposed Replacement Investment:

Cost of new machine 32 (depreciable outlay)

Networking Cost 0.5 (depreciable outlay)

- Proceeds from sale of old machine 9 (current market value)

+ Taxes on sale of old machine 3.12 (tax to be paid)

Initial investment 26.62

Taxes on sale of old machine = (Sale Proceeds – Book Value) x tax rate

= (9 – 1) .39 = 3.12

Cash inflows of the replacement decision at the end of year 1, 2, 3 and 4 are

The new machine will be depreciated in 4 years thus each year the depreciation amount will be

32.5 / 4 = 8.125

The depreciation the old machine would have claimed = 1m (book value) / 4 years = .25 m

Thus the replacement decision will have a net depreciation of 8.125 - .25 = 7.875

Thus Tax shield (@39%) will be = 3.07

Inflows

Year 1

Year 2

Year 3

Year4

Operational Saving

8m

8m

8m

8m

Tax Shield

3.07

3.07

3.07

3.07

Total Inflow

11.07

11.07

11.07

11.07

Since there is no salvage value of any machine thus that would make no difference.

Thus, the cash flows are:

Initial Cost Outlay - 26.62 m

Year 1 11.07m

Year 2 11.07m

Year 3 11.07m

Year 4 11.07m

Thus NPV and IRR can be calculated through excel ( Plz refer Sheet 2 in excel file)

The NPV of the replacement decision is 3.16m

The IRR of the replacement decision is 24%

An3(b) The new machine saves $32 million over the next four years and has a cost of $32 million. Even when we consider the time value of money, the NPV is positive. This is so because the new machine apart from saving 8m per year (operational), also saves 3.07m every year ( Tax shield) due to high depreciation claim it can make.

The effective annual rate of intrest is approximately 6.1 %.

Solution 1(b) In this question we need to find out the annuity amount of 7 annuities compounding at 7% for 5 years.

The annuity is due at the end of the year thus it’s an ordinary annuity.

The annuity value is 8750

Solution 1© The present value of the residual value of the machine after 8 years discounted at 8 % will be given as:

Solution 1(d)

9 % yearly rate can be written as .75% (9/12) monthly rate.

Thus to pay 750000 now at i = .0075 in 36 installments, the annuity amount will be calculated as:

As the annuity was due at the start of the year we used the formula for due annuity.

To calculate the outstanding balance after 1 year, we will calculate the value of 750000 after 1 year at 9% and from this value we will subtract the future value of the 12 annuities that would have been paid in a year’s time.

The loan amount of 750000 will be 817500 in a year at 9% rate.

In one year 12 monthly installments of 24270 each, compounding monthly would have yielded 300948.

Thus after one year the outstanding loan will be = 817500 – 300948 = 512552.

Ans 2- Solution to the problem 2 is in the attached excel file.

PBP calculation

Since there are no formulae for PBP and discounted PBP in Excel, These calculations are shown here.

Project A

Discounted

Initial Cost

-1000.0000

Inflow at the end of year 1

250.0000

224.2152

Inflow at the end of year 2

300.0000

241.3079

Inflow at the end of year 3

350.0000

252.4896

Inflow at the end of year 4

400.0000

258.7978

The rate is 11.5%

PBP for project A

Payback in first three years = 250 + 300 + 350 = 900

After year 3 the remaining amount to be recovered = 1000 – 900 = 100

The payback in year 4 = 400

Amount to be recovered in year 4 = 100

The proportion of year 4 to recover 100 = 100 / 400 = .25

Thus PBP = 3+.25 = 3.25 years

Discounted PBP for project A

Since the NPV in four year is negative, the discounted PBP cannot be calculated.

Project B

Project B

Discounted

Initial Cost

-1000.0000

Inflow at the end of year 1

400.0000

358.7444

Inflow at the end of year 2

350.0000

281.5259

Inflow at the end of year 3

300.0000

216.4196

Inflow at the end of year 4

250.0000

161.7486

The rate is 11.5%

PBP for project B

Payback in 2 years = 400 + 350 = 750

Amount to be recovered in the third year = 1000 -750 = 250.

The amount recovered in year 3 = 300

The proportion of the year 3 to recover 250 = 250 / 300 = 5 /6 = .83 years

The PBP for Project = 2+ 0.83 = 2.83 years

Discounted PBP for Project B

Discounted Payback in three years = 856.6

The amount to be recovered in year 4 = 1000 – 856.6 = 143.4

Discounted Payback in year 4 = 161.7

The proportion of year 4 for recovering 143.4 = 143.4 / 161.7 = .88 years

Thus the discounted PBP = 3 + 0.88 = 3.88 years.

Ans 2(b)

If the projects are mutually exclusive we can invest in only one of the projects, thus we need to rank order the projects. In such situations it may so happen that NPV and IIR clash i.e. both give different results, in such a situation NPV takes precedence over IRR as it is more consistent with the wealth maximizing principle. However in this case both NPV and IRR give the same result i.e. Project B is better than project A as only it has positive NPV and only it’s IRR is higher than cost of capital.

If the projects are independent, selection of one project does not affect the selection chances of the other projects. The evaluation of projects is done solely on the basis of their IIR and NPVs.

Going by both the NPV and IRR rules

Project A cannot be undertaken as The NPV is negative ( -23.2) and IRR is also than cost of capital ( 10.48% < 11.5 %).

Project B can be undertaken as it generates positive NPV (18.4) and IRR is also higher than cost of capital (12.44% > 11.5%).

Yes it is better to get large cash flows early and tail off later or to get large cash flows later in the project life cycle because that would offer more money to be reinvested at the earlier stage which will generate more value. Even in these two projects though the sum being returned is same i.e. 1300 but since project B gives larger sums in the initial years it offer higher IRR, MIRR and NPV.

Ans 3

Assumptions:

Depreciation on old machine is calculated considering the book value for next 4 years.

Depreciation on new machine is calculated considering the purchase cost for next four years.

Initial Investment

(a) Initial Investment for the Proposed Replacement Investment:

Cost of new machine 32 (depreciable outlay)

Networking Cost 0.5 (depreciable outlay)

- Proceeds from sale of old machine 9 (current market value)

+ Taxes on sale of old machine 3.12 (tax to be paid)

Initial investment 26.62

Taxes on sale of old machine = (Sale Proceeds – Book Value) x tax rate

= (9 – 1) .39 = 3.12

Cash inflows of the replacement decision at the end of year 1, 2, 3 and 4 are

The new machine will be depreciated in 4 years thus each year the depreciation amount will be

32.5 / 4 = 8.125

The depreciation the old machine would have claimed = 1m (book value) / 4 years = .25 m

Thus the replacement decision will have a net depreciation of 8.125 - .25 = 7.875

Thus Tax shield (@39%) will be = 3.07

Inflows

Year 1

Year 2

Year 3

Year4

Operational Saving

8m

8m

8m

8m

Tax Shield

3.07

3.07

3.07

3.07

Total Inflow

11.07

11.07

11.07

11.07

Since there is no salvage value of any machine thus that would make no difference.

Thus, the cash flows are:

Initial Cost Outlay - 26.62 m

Year 1 11.07m

Year 2 11.07m

Year 3 11.07m

Year 4 11.07m

Thus NPV and IRR can be calculated through excel ( Plz refer Sheet 2 in excel file)

The NPV of the replacement decision is 3.16m

The IRR of the replacement decision is 24%

An3(b) The new machine saves $32 million over the next four years and has a cost of $32 million. Even when we consider the time value of money, the NPV is positive. This is so because the new machine apart from saving 8m per year (operational), also saves 3.07m every year ( Tax shield) due to high depreciation claim it can make.