Live Co$.,$ an app developer, has developed a new app, $$Lingo$,$ which it plans to launch in the near

future. Sales of the new app are expected to be very strong, following a favorable review by the

media. Live co$.$ has been informed that the review will give the app a $$Best Buy$$ recommendation.

Sales volumes, production volumes and selling prices for $$Lingo$$ over its four$-$year life are

expected to be as follows:

Year $1234$

Sales and production $($units$)137,500100,00090,00087,000$

Selling price $($$ per game$)$ $$26$ $$25$ $$23$ $$23$

Financial information on $$Lingo$$ for the first year of production is as follows:

Direct material cost: $$7\mathrm{.}30$ per game

Other variable production cost: $$6\mathrm{.}10$ per game

Fixed costs: $$3\mathrm{.}75$ per game

Production costs are expected to increase by $7\mathrm{.}5\%$ for the first two years of production and will

remain the same for the last year.

Advertising costs to stimulate demand are expected to be $$450,000$ in the first year of production

and $$225,000$ in the second year of production. No advertising costs are expected in the third and

fourth years of production. Fixed costs represent incremental cash fixed production overheads.

$$Lingo$$ will be produced on a new production machine costing $$850,000,$ and the company intends

to sell the machine at the end of the production run for the price of $$50,000.$ The sum will be

received in whole, one year after the sale is made.

Live Co$.$ pays tax on profit at a rate of $30\%$ per year and tax liabilities are settled in arrears. Live

Co$.$ uses a discount rate of $12\%$ when appraising new capital investments.

Required:

a$)$ Calculate the net present value of the proposed investment.

b$)$ Calculate the discounted payback period of the proposed investment.

c$)$ Calculate the IRR of the proposed investment.

Live Co$.$ also had a parallel project running on the side called $$Ace$.$ Investment appraisal of $$Ace$$

showed, expected initial investment cost of $$750,000,$ NPV of $$10,500,$ discounted payback period of $3$ years and $2$ months, and IRR of $18\mathrm{.}5\%.$ The company decided to shelf that project and go

ahead with $$Lingo$$ instead, due to mixed reviews from the press for $$Ace$$ and citing improving

economic conditions. Live Co$.$ is highly liquid and has excess cash in its financial statements for

the foreseeable future.